IF YOU TWO ARE OF EQUAL SKILL, YOU'RE GOING TO HAVE TO WORK TWICE AS HARD JUST TO KEEP UP.
But na, seriously.
Doc vs Fox.
In reality, it's probably a 50/50 matchup. In my opinion, it'd be 45/55 Fox.
The way this matchup works is kinda like this; as long as Fox wills it, Doc has to play at Fox's speed. Fox wills this by how aggressive he plays, or how much he runs away (when applicaple), but that's it.
Just like pretty much every matchup (just like alot of matchups in all fighting games) there are pretty much 3 basic levels, close range, mid range, and far range.
At far range, Fox keeps control over Doc. Yes, lasers are completely avoidable at every turn (read: Fox REALLY cant laser camp you unless you let him), however, fox can actually punish Doc from far range, where as Fox has to be asleep at the wheel to get punished by Doc at this range. Now, for people who dont understand what punishment is, punishment is simply getting a guarenteed hit (or action) for an action (or lack of) from an opponent. With this being said, the one thing Fox can punish from a far range against doc is pills. If doc goes to throw a pill and fox calls it, Fox can punish with lasers every time. However, Pills stop fox from freely running in or jumping around; therefore, you cant just completely ignore abandon pills. So at far range, you're main goal is to avoid allowing fox to tack on damage with lasers. This can be as simple as going into shield. You can cape lasers if he's doing any sort of jumping laser. Go ledgestall to get away from them, jump on platforms, there are plenty of things you can do, you're just looking to not take a crapton of damage from lasers. Infact, if you can predict fox overcommiting to lasers, you can just take the hit and go in there; it's not like the lasers actually STUN you or anything.
Next range you have is midrange. There is where I start to say things lean more towards fox. At this range, Fox is an easier time getting in, gets more of a reward on hit, and can defend himself better than Doc can. It's not to say Doc cant win at this range, oh doc can annhilate fox, but it's easier for fox to win out. On Fox's offensive, you will mainly have to contend with n.air, d.air, grabs, JC Upsmash. First and foremost, understand that yes, grabs are viable for fox at this range because of his ground speed. The faster one's ground speed is (dash speed included), the longer their grab range is because the less time you're going to have to react to them coming in (dont confuse this with somebody's grab reach, completely different stat). Anyway, at midrange, you have to look for the one move that beats shield, grab. You also have to look for n.air, which if fox comes in close enough or FH, beats out alot of things you can throw at him. From this point, you can beat a n.air with an u.tilt, a well placed u.smash, or at correct percents, CCcounter. If you call him jumping, you can beat him with a FH D.air. If you're looking to just flat out challenge his nair, you've got your b.air (if you're facing backwards), or n.air.
On your offensive, all you really have is FH d.air (which again, is more of a defensive maneuver), n.air, b.air, and f.air. Realistically, you shouldnt be allowed to come in with a f.air. Windup is too long. If you can land one, even on shield, that's great (although Fox is one of the few characters that can beat you out of shield easy), but if you can put a f.air on him, more power to you. So realistically, you have to resort to your other moves, which means you're actually doing an aggressive defense.
*Note* When I say FH D.air, i mean FH d.air, not FHFFL d.air, nor do I ever talk about SH d.air. I think both of those are pretty terrible. FHFF D.air that is autocancelled is acceptable, but but FHFFL d.air -shakes head-.
Fox at midrange can pretty much pick a move in his arsenal to play defense with. As long as it hits hit, it'll pretty much work. And then, because of his dash speed and Doc's lack of range, moving out is always a viable option at this range. So not only do you have to worry about will you hitshield or will he evade, you have to worry about will he make you wiff. With this in mind, you dont want to do alot of midrange attacking.
Close range, this is where things start looking up for Doc.
At this range, you get the meat of your offense. Your grab game comes into effect, jab game comes into effect, defense gets stronger, yadayadayada. However for fox, pretty much his stuff is as strong as it will be already.
*Note* For the record, again, because of fox's speed, his "Close Range" is actually bigger than Doc's "Close Range". Its a matter of reaction times.
At close range, Fox actually has to read Doc's offensive mixups. He has to deal with Jabs and Grabs, he has to be weary of being wiff punished, since Doc can is going to naturally be more active, Fox actually has to play some real defense at this point. Now, lets clear something up, once you're in this range, Doc has to deal with Fox's greatest offensive weapon, Fox's D.air. You cant CC it, and it's pretty much safe (by way of shine), and if you get hit, that's a guarenteed grab at the least for Fox. So it's not like Doc dominates the close range or anything.
But what Doc gains in this range is his grab, which can lead to a stock in various situations through way of Chaingrabbing or real good tech chasing (I advise you to TAKE THE CHAINGRAB WHENEVER YOU CAN, DONT BE A HERO). Doc's grab can also lead to edgeguarding at pretty much any point, and can lead to kills 'round 100% or so. Fox's grab game is not anywhere as strong.
At this point, Doc can look to clear fox out of his space with d.smashes or tilts. Fox can do the same (Random Note: I dont know why Fox players dont actually D.smash more as to catch people with bad DI. You have to DI d.smash in, and you have to DI U.smash out.). Again, where fox loses out in this range is the fact that his grab game isnt anywhere as strong as Docs.
So, that's pretty much the range game in a nutshell.
Next thing you have to worry about is positioning. Platforms are going to help Fox more than they're going to help Doc for pretty much one reason, it stops Doc's chaingrabs. Doc also suffers from having some difficulties following combos onto platforms, but that's nowhere near as bad as having CGs broken up by platforms. Beyond that, platforms are pretty much the same for both characters. Fox natually has a stronger game coming up through platforms because his u.air can kill, and can do more in ways of coming down since he falls fast, but it's nothing to throw up red flags over.
Doc's edgeguarding is so good. Doc's recovery is so bad. In the end, it's almost like saying once somebody get off the stage, you can almost say they wont come back.
The one thing Fox does to screw up a Doc edgeguard is Illusion. It's not as if it shuts down doc's edgeguard, but it forces Doc to make choices, and wrong choices allow Fox to come back and convert. Doc has to look for an illsion anywhere from above the stage (especially if it can lead to a platform cancel) down to a sweetspot. Realistically, Doc is only allowed to guess once because one he swings and misses, Fox can just come in. There are acceptions to this (the main one being if fox would illusion, not hit a platform cancel, and not hit doc). So basically, the best way to setup to stop this is to have your back towards Fox. If he comes high, you have a b.air, if he comes at you, you have tilts, and if he goes for a sweetspot, you again have b.air and tilts (or WD onto ledge if you're fast enough).
The next thing Doc has to read is Firefox. What's important about reading this isnt specifically the location, but moreso of how far Fox is away from the ledge. The first thing to know is that if Fox cant immediately grab the ledge, or if he's close enough to where Doc can jump out and b.air, Doc outta jump out and b.air. Just cut out the middle man, take out the guess work, put the Fox down or in a worse position. If that cant be done, this is where the question reading an analyzing comes in. Doc has to note things such as
-Is fox above the level or below the level
-Has this person tried anything "Crazy" before
-How many angles can I cut off
If fox is above the level, then you have to throw in the possibility that they're going high. Lets be real, Doc has a cape, and it's no secret. It's not like somebody is going to be crazy and go straight into you.
But that goes into the next thing. If you didnt stop them the first time, or if you completely ****ed up the cape, how in gods name are you going to be sure they wont try it again?
So can you jump out there and b.air cape before they get in? How many angles can you cut off relative from where they're at? Stopping a fox isnt as simple as "He's going to Firefox, so that's an automatic cape." People just arent that stupid. You want to try to make the cape as easy as possible, so you want to try to force them to have to go into you, and not have to fall at all (because if they fall, they can change their fall speed).
What's easy for Doc depends on player to player. I actually blow horribly at caping, so I look to just take it out of the equation period and work from there. Then you have people like Greenmario (yes he's a mario, they do the same thing), and he can pretty much nail every 50/50 cape he's setup with. It's preference. You gotta figure out what works for you
Now, as for Fox edgeguarding doc, this gets bad for Doc. Fox has 10 ways under the sun to keep his invincibility. Doc's recovery is bad. Therefore, if fox is on the ledge when Doc comes back, Doc is more-than-likely going to die. What this means is that doc wants to do everything in his willpower to get Fox off of the ledge. If Doc comes high, he wants pills. If he has to come from a lil ways out, he might try to tornado and scare fox into moving (yes scare, this really shouldnt work). But he just wants fox to move. You cant do a "if you're coming from below", because again, Doc's recovery blows. So Doc has to try his ****edest to keep Fox off the ledge, or beat him to the ledge. All fox has to do is land a shine and he wins. Fox can do so much more to get rid of doc, however. Fox can land a b.air from anywhere (that even includes straight up ledgeDROPPING a b.air, and then recovering. I've seen it done to myself many times, it's that easy to stop doc). Fox could go as far as to just jump out and n.air if he really wanted to, there's not alot Doc can do about it at this point.
Some last random *** notes.
This has been said a few times, but it cant be stressed enough that Fox's grab game vs Doc is not that good. I wont go as far as to say it's horrid, cause I honestly understand the concept of a good character, but it's safe to say that his grab game isnt stellar. With that being said, it also has to be noted that Fox has a kill move from the ground (u.smash) and in the air (u.air). My point is that in situations where you would die, it's ok to lean towards giving up a grab as opposed to giving up a hit. You have to realize that if fox grabs you, it will lead to more damage; maybe an edgeguard if you're close enough to the edge. However, if so much as get jabbed in those same situations, you stand a good chance of catching an u.smash at this point. So it's safer to give up a few numbers than to give up a head.
I guess I should go back and clarify something. Fox's grab game isnt so good because there isnt a % where Fox can do u.throw u.air on doc AND KILL. Now, that's not to say Fox can never do u.throw u.air, that's a lie. Fox can do it, it just wont kill. That's not to say he cant predict a move and punish accordingly (which is what comes from his u.throw at kill %s, since again, fox has no guarenteed u.air at this point), but Fox cannot flatout throw doc up, and then follow him up for a guarenteed u.air for a kill. With that being said, Doc actually has to do work to not allow Fox to do this anyway. Doc has to be ready and willing to jump out, n.air/d.air, do something to keep from catching the u.air. However, there really isnt one thing that winds up being a catch-all. Fox has a few other things he can do to still land his u.air. He can wait for a jump, he can do something else to punish an aerial, etc, etc.
So yeah, in conclusion.
Far Range: Fox controls and can punish Doc. It's nothing game ending, but it can happen.
Mid Range: Fox gets the meat of his offense, Doc has to rely on mostly defense.
Close Range: Anybody's game. Doc's offense gets buffed, but Fox's stays fairly close to the same, which is going from **** to ****.
Grabs: Doc loves em. Fox is like "Meh, it'll get me to my goal in the end"
Platforms: Nothing special. Fox gets saved from chaingrabs, but doesnt specifically get a big buff from them or anything. Doc is always hit-or-miss with anything beyond grabs and combos.
Edgeguarding: Put Fox here, dont let Fox put Doc here.
Is that enough?