A little background. I've been playing Ness since N64, although only locally and not exclusively. My little brother is the best smash player I've ever played, and he might say the same about me, although he is slightly better. We play PM all the time, and Captain Falcon is one of his main characters in it. That, and the fact that he's been playing against me / Ness for, like, 2 decades makes this an insanely hard match up for me. So, what I think about the MU.
Neutral: His dash dance combined with his speed and air priority means Captain Falcon is constantly representing a threat and baiting you to make a mistake. Your reactions must be very tight, and you need to know your options well if you don't want to taste the wheel of pain. Many of your ground moves are non-options as throwing them out is going to gain you a drive by dair, and only that if you're lucky. As has been said, your PKF spacing game is very important here, try not to throw out grounded ones unless you know they'll hit. What you really want to land on Falcon is a throw, but many of his attacks (all his aerials) are going to push you far enough that a shield grab is unlikely, if spaced well, or have him end up far enough behind you so as to be unpunishable. That, and CF wants very badly to grab you. A good falcon can land a single grab, and start a chain of down throws, Nairs and gentlemans to carry you across the stage and end the whole thing with a throw into knee attempt. I would not DD much, as it feels too slow in the MU and easily punished. Nor do I use psi magnet to attack in the neutral game, as it loses to most of Falcon's air moves. Now the good news, Captain's most effective entries are horizontal in nature, and once he tries to act on something he is pretty committed to it. So, you basically know that regardless of your height, his action plan is to fly (more or less) right into your face. Good aerial PKFs, Magnet momentum stalls (not too often) to throw off prediction, and carefully placed Nairs and DJC Fairs are your action plan until you can land that precious grab. Nair OoS if you find yourself under a lot of pressure. At very low percents, if you find yourself within range next to a shielding falcon that you've been applying pressure to, try spamming down tilt until you rack up 15-20 percent, and then stopping suddenly and dash grabbing them. This is by no means a sure thing, but it is an interesting mix up that applies psychological pressure as well.
+1 Falcon, pressure is on you to play more perfectly and not get put in a punishment combo first.
Combos: Let's start with throws. Down throws at low damage can be chain grabbed against a Falcon who doesn't SDI forward from you, and then you have the tech chase if he does do that. I've never thought to follow up a poorly DI'd down throw with a DJC up air into regrab, will have to try that one, Bry. Personally, I like to mix up my game with up throws so my opponent can't get too used to the responses demanded of the down throw. At VERY low damage (like 0) I don't believe there is a follow up to Up Throw > DJC Up Air, so what I like to do is Up Throw > Full Hop > Psi Mag > DJC Fair / Nair which will often put Falcon slightly off stage or have us land together with me in a tech punish scenario. As you rack up damage, up throwing becomes a nonbo, where as down throw will set up a nice edge guard scenario, just SH Mag > DJC Nair and proceed to the next section. Side notes on combo'ing CF. Up Smash and Running attack pop Falcon up to the perfect height for bair punishes, but they're not exactly reliable or easy to hit, you need a seriously good read on your opponent. I have comboed INTO these attacks, but it's never a sure thing, I'm just saying to be mindful of your options and practice the matchup so you can see the opportunities coming. Your bread and butter here is gonna be DJC fairs and Aerial PKF's into grabs that start your combos, so rely most heavily on this.
+0.5 Falcon, Combos are what both of these characters are about, but Falcon is a glass cannon that fires combos. Ness isn't going to Zero to Death Falcon without him ever leaving hitstun. Ness combos into his ledgegame, not into a stock.
Edgeguarding: Some more background. We have a pretty strict honor rule of "no intentional edge hogging" for friendlies in my group. It makes the games more interesting and fun, and I believe it makes you more mindful of your options and trains you in what your characters are capable of off stage. We also go out and spike people who were going to die anyway, to give your friend an honorable death. So, that being said, I play off stage a lot with Ness, and very aggressively pursue my kills. So, options. For a Captain Falcon who is not particularly good at recovering exactly (or if you are particularly skilled with your timing) using Down Smash to hit Falcon's knuckles as he reaches for that ledge is an effective and safe option. Against most characters a psi magnet intercept into rising dair is wonderful, but you may find yourself boosting the raptor back onto the stage so be careful when using an option like this. A dangling Up Smash can catch unwary opponents off guard, and net you a free kill out of sheer surprise. I think there are percentiles where it will stun Captain so long that by the time they can Up+B they will actually fail to recover, but I'm not sure. But, I do know that sometimes, they won't be able to Up+B before I can run off the map, and stage spike them with a Bair. In any case, Up Smash is a very safe option and worst case scenario it just bought you a bit of percent and they get onto stage / ledge. Don't start it too early though, because they will try to go over you, if possible. If you hit them into the upper corner of the map so that they are forced to use Falcon Kick to recover, this is when you bust out the PK Flash, as their recovery becomes very predictable. If you can line up an off stage PKF, that is free Dairs, and will net you a kill if you know the PKF timing. My most used options are to pursue off stage and delay my fall with multiple Psi Mags and basically cover all of his options of recovery and threaten a rising bair at every avenue of escape to ensure my kill OR grab the ledge repeatedly and simply dair, bair or ljc into either of those moves. Be mindful of when Falcon actually has options to recovery, especially his walljump options. Lot of options here for Ness as well, play to your style, but try not to get predictable.
+0.5 Ness, while Falcon's stomp and knee are way more likely kill, we have far more versatility in our intercepts and depth for pursuit, and Falcon is far more easily gimped, even by a paltry psi magnet.
Recovery: First thing's first, if you have gotten knocked off the stage and the Falcon player sitting next to you is doing his job right, he has just lined up a kill attempt. If you got popped up by something that sends you not far in front and above of CF, SDI away and down to try and sour his knee if not dodge it completely. Still alive? Good, but don't relax yet. Did he jump off stage after you? If so, be careful, he may try to stomp or up air you with his double jump on his way back to the stage. If he is off stage with you and you avoid the intercept (or dair him on your way back) you should make it back on stage alive. If he did not pursue off stage, ask yourself a couple questions. Do I have to use PKT2 to survive? Am I so low that I cannot attempt a platform recovery or to sweet spot the ledge? If the answer to both of these questions is yes, you may be in some trouble. Ness's airdodge is wonderful in his recovery game, especially against captain falcon who has to commit like a mofo to intercept you. PKT2 is pretty mediocre as far as being punished is concerned, in this MU. So, do not expect to get away with doing it poorly a lot, especially from below the ledge. If your opponent is interception crazy you can try Psi Mags to throw off his prediction, but don't do this too close to the stage. Expect the punishment if your opponent is at all familiar with Ness.
+1 Ness, Ness's recovery, while punishable, has incredible range and far more versatility than Falcon's. No contest.
Stage Choice: I wouldn't listen to me much here as this section is going to be highly colored by general personal preference on the maps. I don't like high platforms because they can interfere with up throw combo game, but super low platforms can be just as bad as it can even further limit your approach options and eat aerial PKF. Close blast lines on the sides favor Captain Falcon, I feel. Level ground is important in the match for the few times you utilize ground PKF, but we're not the tallest so the uneven floor can interfere with Falcon's grab game as well.
Neutral Stages in order of preference: Smashville > FD / PS2 > DL > BF > FD > YI
Counter Picks I just like: WW, GHZ, DC, and MM
Maps that just randomly kill me by tucking me under the stage with my double jump: Sky World, Lylat Cruise >:[
Final score, 1.5:1.5. I would say the match up is 50/50, and I think it really goes to the better player, not the character. Whoever has the more extensive knowledge of what both characters are capable of, the better read on their opponent and the better technical ability is going to take this fight.