The biggest problem I have against Falcon is landing. I faced one with impeccable dash grab timing that had his hands on me as soon as my feet touched the ground. It didn't matter if I covered my descent with N-air or empty landed into jab, he'd always get me. I had to give up doing full hop F-airs because of this. Any advice?
Go off stage and grab the edge. Sometimes it's safer than landing on stage.
As for the Falcon MU, I would say I have a decent amount of experience in it. My cousin plays Falcon (he's decent) and I've played some local Falcons here in Toronto.
I would say the MU is 55-45 or 60-40 our favor.
Let's start by discussing the neutral. The neutral game honestly isn't that bad for us. Falcon has a hard time getting in while you can short hop retreating fairs to pressure and retreat. If Falcon is dashing at you, they will usually go for a dash grab, dash attack, or shield roll. Dtilt or jab beat grab, clank with dash attack and have low enough recovery frames to not get punished by dash roll. You have to be careful though, because Falcon's dash grab is exceptionally fast and timing is key. If Falcon decides to jump and aprouch, utilt will stuff him out. You can also play the neutral somewhat aggressively, keeping Falcon at tipper range and pressuring him closer to the edge. He has a very hard time getting past dtilt and spaced fairs. Most will resort to rolling out when feeling too pressured. If you can read the roll, it's simple to punish.
Though I've been talking about the neutral from Marth's perspective, I do have some experience on the opposite side too. I know I said dtilt beats out most of Falcon's options from Dash but it's tricky to get the timing right. As Falcon, I like to dash, jump back, dash, jump back a couple of times just to keep my opponent guessing when I will approach. This baits some less proficient Marth's to throw out attacks such as Fsmash which can be punished. Also, I like to use the pseudo dash dancing to keep Marth's guessing when I will approach and vary up my timing. This leads to a higher success rate when I do decide to actually dash in for a grab or dash attack.
All in all, I would say the neutral is fairly even. Now, let's talk about the punish game.
Falcon punishes Marth hard. Most if his hit confirms and his grab lead to his uair juggles which can rack on a lot of percent. Marth has a hard time landing so I would suggest trying to land on stage once to see how good the Falcon is at juggling and if he's good at it, then go for off stage edge grabs.
MAKE SURE YOU DON'T LOSE YOUR JUMP IN HIS UAIR JUGGLES. Despite his hard punishes, Falcon has a surprisingly difficult time killing Marth. This is his downfall in the MU. His best killing move is his bair. It's fast, and reliable but gets stuffed out by Marth's fair, ftilt (if you're on the ground), or can be countered if you're feeling bold. His bair can't be combo'd into and is often telegraphed when he's about to do it. His other kill options are laggy and easy to punish. Knee is unreliable. Falcon can dthrow → knee or Nair → knee but these work at lower percents and if you're not right on the edge of the stage or have horrible DI, you should survive. Falcon's knee combos stop working pretty early in percent or when he's built up enough rage. Here's a tip for you Marth mains. Most Falcons will go for the knee even when it's not a true combo. Once you learn the percents at when knee stops working, you can DI poorly on purpose to bait the Falcon and counter the knee. This will kill Falcon at around 80-90%. As for the other kill moves, raptor boost is laggy on shield and very easy to punish. Just be wary of it at all times. Falcon's back throw can also kill if you're near the edge. This only works at higher percents (150+) but it's something to note. Falcon's Fsmash is laggy and easy to punish but you have to be very cautious of its range. Some Falcons like throwing it out when you're getting up from the edge, if that happens, just wait or counter. Falcons other smashes aren't reliable kill moves and are laggy. One thing to note is that uair can kill at high percents (160ish). Don't let the damage build up too fast.
Marth doesn't punish Falcon all that hard but honestly, it doesn't matter. You should only have one goal as a Marth main and that is to get Falcon off stage. Luckily, Marth is well equipped to do just that. At low percents, dthrow → bair is a reliable combo and sends Falcon a decent distance towards the edge. It can also be followed up by fair or fast fall uair most of the time. At zero, fthrow → fair isn't bad either and fair can be linked into other fairs. You can also start juggling Falcon with dthrow → uairs and set ground traps to build up percent and make it easier to throw him off stage. Once Falcon is off stage, it is a very simple edge guard. Just swat him away and hold the ledge, then follow his movement. If he decides to go low, drop down and bair. If he goes high, get off the ledge, jump and bair. Rinse and repeat until he's dead. Sometimes the Falcon will try to recover high so you can't edge guard him. Usually he'll do a Raptor boost or very high Falcon Dive. Don't fret though, both of these moves are easy to punish. Get off the edge early when you see him recover high so you can maximize the time you have to punish. You don't want to start dashing and chasing him, that's how you miss punishes. Once you're in place to punish, don't just go for Fsmash as that's not your goal. Remember, you want to get him back off the stage. If you're proficient at doing it, you can run pass, turn around, tipper fsmash to get him off the stage. If you haven't practiced this enough though, there are other options. Grab works but you don't get Falcon that far off stage and he can easily recover before you have a chance to set up a solid edge guard, so don't go for grabs unless the Falcon is at high percent. What I like to do (if I'm not running past → Fsmash) is run past and dancing blade (DB). DB is a fairly good punish, dealing more damage than just a grab, and DB forward 4 has more knock back and at lower percents, it's easy to link all four hits. Basically, at higher percents grab and at lower percents, DB to get the Falcon off stage. Also if possible, when Falcon is recovering, don't throw out attacks until Falcon does a Falcon Dive . This will prevent the Falcon from air dodging through your attacks and recovering.
So all in all, I'll repeat that I think this MU is 55-45 or 60-40 Marth's favor. The neutral game is pretty even. Falcon punishes Marth hard but can sometimes have trouble landing the finishing blow. Marth on the other hand, has an easy time gimping Falcon. All of this came from my experience playing and playing against both characters so feel free to correct me if I am wrong about anything or add to my arguments.