You're both looking for similar things on this stage. If your opponent takes to the air, juggle them or get a hit like uair or fair or single hit nair that can lead into a grab. Primary approach tools for both of you are grab (though you have dtilt as well). Both of you may also try approaching with or controlling space with nair, and in your case, it's stronger here than in other MUs. AC nair is very strong vs Falcon compared to other characters in the higher tiers.
Again, similarities between the characters, both of you will want to dashdance approaches that aren't overshot, and shield to immediate WD OoS when they come in closer (unless CC is available, it always hit against first hit of nair from either character).
Fthrow is better for tech-chasing than dthrow, as a general rule, but unlike dthrow, it doesn't knock down at zero (dthrow becomes a stronger option when your back is closer to the edge).
An AC nair in place can cover most jumps towards you, and is effective vs grab approaches, but be prepared to drift backwards, and then shield DI back in if he tries to punish the nair. Dashing forward after this can counter attempts to run in and grab, and isn't as big a commitment as wavedashing, spotdodging, or rolling to escape. Alternatively, ac nair with jabs and dtilt makes a great wall, and you can easily space for position with Dancing Blade similarly fast, but if it causes falcon to land shortly after hitting, it tends to be a worse option.
This AC nair + otherstuff wall not only beats many approach options, but leaves you with enough time to punish or safely space should falcon try to maneuver around it altogether. If falcon doesn't try to punish/move around it or get behind you either watch what he's doing to pick up on what he likes to do, or push forward and whatever pace you can comfortably. More likely than not, you can get a lot of Falcons to play in shield more with these tactics, but this can be beaten out with well timed punishes, and with falcon's tilts (or fsmash).
Falcon's super fast and has a good grab game against you, so try to stick to lower commitment moves and keep barely out of his reach either framewise or spacing wise.
While dtilt is amazing, if Falcon buffers a roll away out of dtilt on shield, don't even bother trying to punish, at least not directly.
While Falcon's dash dance is amazing, he sticks his foot back a little at the beginning of the dash and the hurtbox stays there. When he dashes back from a dash forward, his foot starts from a similar horizontal position to his head. You have a dtilt, exploit this, and take stage position.
Don't be afraid to counter. Falcons love aerials. Even still, this is something you might want to do more against attempts to space well where Falcon's trying to cover whiff punishes.
If Falcon tries to nair in place or retreating (or any aerial really), this makes it easier to land moves normally riskier in the neutral, including fsmash, which will knock him down, and possibly make your opponent feel stupid. Refrain from using this move outside of tech-chases, combos and edgeguards until you can confidently use it on reaction to knowing where Falcon will end up if he goes forwards, or otherwise only when he isn't moving forward.
-I'd say mostly abuse AC nair/jab/dtilt wall and shield+wd OoS when you can't grab immediately are the biggest things for neutral, along with trying to dash forward towards Falcon with his dash back (for trot can avoid his JC grab back towards you, or you might try shield stop nair in place-> continued wall. If he's slightly farther away, run-crouch dtilt is an option, but it's harder to get this when his DD is good, shield stop grab or dancing blade are acceptable when he turns around before you can dtilt). Nair a little less if Falcon tries to just space his tilts against you or start hit nair as you're coming down. Try to react off of what Falcon does when you apply pressure (or limit his methods of approach). Throw tech-chases at zero are escapable if Falcon isn't close to the edge. CC is really strong. Be ready to shield any OoS options Falcon puts out if you can't dash away safely in time. More than anything else, try to avoid getting grabbed. Space yourself and position hitboxes to avoid this as best you can.
