The basic mixup with lasers is that you can raptor boost under high lasers, and nair over low ones. I like to PS laser into grab, and when you get them on tilt, PS their laser to lock them down and follow up with nair/uair/knee/bair(reverse bair). Also, don't be afraid to eat a laser, just make sure they can't use it to follow up into crazy Falco combos.
For utilt, space an aerial, you can actually knee them for free if you're timing and spacing are on point. You can also jump past it and bair them, but that's harder than just spacing a knee, bair or uair IMHO.
Don't be afraid to platform camp. Forcing him to come up towards you can be used to bait him above you, or you can take that opportunity to space stomps around his approaches (preferably with edge cancels). Also shield drop uair is super useful, as is just vertically crossing up with uair, but like anything else, don't let your opponent bait it out of you.
Also, trades favor Falcon cause you can kill Falco so early, while Falcon is a tank with proper defensive tech.
As far as Defense:
SDI/ASDI out of pillar combos, if you are able to SDI hard enough, you can get out pretty early and consistently, and utilize platforms to mix up your position and techs. It's very complicated but you can also use no tech-> slide off edge to recover very quickly out of combos and keep yourself moving. PS shine helps with getting out of shine pressure, as does using light shield (both have increased knockback so you can Shield DI out of their shine range earlier). If you PS the shine, you can gentleman both spacies, and against falco you have enough frame advantage to grab, since Falco's multishine is a few frames slower than Fox's.
Edge Guarding:
So much easier than Fox, if you can get Falco below the stage you can just poke him out of his Firebird with either bair, soft knee, uair... whatever you'd like really. Just watch for the dj sweetspot and side b. I usually cover side b with an edge cancelled bair or stomp (facing into the stage) and then follow up from there. Grabbing ledge is also useful. (E.G. Grab ledge-> dj autocancelled bair onto stage-> pivot downward angled ftilt-> run off uair/knee)