In this matchup you want to avoid being grabbed, particularly in starting percents to 30%. I say 30% because if he gets his first dthrow grab on you at 30%, it won't be decayed enough to do the full CG on you, leaving his CG at around 40% - 45%. After CG percents, avoid to get dthrow > jab for extra damage into a laser lock IF THE FALCO KNOWS WHAT HE OR SHE IS DOING. Against campy Falcos (which is what they SHOULD be doing), if they attempt to side-b to the other side, you can react with utilt, or with the preferred ftilt since it doesn't stale your kill move and puts Falco in a position to get grabbed or Fair'ed, depending on where they are. In general, you wanna stay in the air unless you wanna go through Falco's lasers powershielding them and predicting the aforementioned side-b and intercepting with ftilt or utilt.
When on the defensive, you want to avoid getting grabbed period. Grabs on you can be really dangerous especially if they Falco knows how to mix up dair tricks into baits and punishes. Use waddles to get 5% or to eat some of the lasers at waist level. Since you are either staying at from Falco or keeping yourself in a position to either block lasers or baiting and punishing side-b attempts.
On the offensive (which you should be since a Falco should never be a approaching), you want to stay in the air. Even though I say this for every matchup, your air options are just sooooo much better than your ground options. Bair > Falco's aerials by a lot. Our bair, when it hits, can be followed up really well, by running and going for the grab. If you get the grab, you can bthrow for the 16%, but you can dthrow and go for the tech chase. When tech chasing Falco, it tends to be your best option to slowly walk forward and wait for the Falco to tech in place or tech roll in front of you or behind you. Since Falco's tech roll is about the same speed as your dash, you can use that to regrab and either bthrow or dthrow again and repeat.
When in kill percents, whether it be you or Falco, you want to avoid getting dair. Please. Don't let him do it. Falco's options after a dair at high percents are ****ing ridiculous and can kill you if you don't know what's coming. If you get grabbed, he will dthrow and try to Fsmash kill you. Don't fall for it. Jump always. When Falco is in kill percents, you want to set up for the kill by ftilt him and trying to bait him to side-b, then punish. Whether or not is kinda important, because he can always just airdodge. If he does, go for the grab and fthrow or bthrow off the stage and proceed to kill him offstage. Remember, ftilt eats side-b and can stop his recovery if he doesn't use up-b to recover.
When it comes to offstage and edgeguarding, you have the upper hand. Falco has to get back on stage the best he can or get 30% easily, whether it be from bair or fair. When Falco has to edgeguard you, I usually tend to up-b into the air and wait for the uair to come and SDI the first hit if he tries to hit you with both hits. Not much to really cover in this section of the matchup.
Overall, 60:40 Falco. We have options, he just has better ones.