what I have found so far is that lasers are only really useful when the opponent is near max range of them (which is silly short now, sakurai plz). Shine is mostly used for spacing because it has a pretty impressive range. Side-B has a nerfed hit box (compared to brawl so i guess you wouldn't notice that) but compared to melee the range is much larger and also doesn't put you in helpless state so he can do some fun things with that. Up-B is multi-hit now and snaps to the ledge very well, still mainly only used if you need to vertically recover.
His tilts are all very good his up tilt has a great hit box in front, reaches quite high above, and lingers for a decent amount of time. Forward tilt has great range and is incredibly quick. Down tilt is weaker than it was in melee but compared to brawl falco's, it is godlike. Along with these, his jab is VERY good, fast, great hitbox, many mixup opportunities. use it!
His smashes are all pretty solid. his upsmash is still very quick and the 2nd hitbox seems to last a little longer than the older iterations of the move, which is nice. however the knock back is slightly nerfed. His fsmash is relatively quick and has solid range and impressive knock back, but has somewhat punishable ending lag. It is completely different from melee. His down smash is pretty much the same.
His neutral air is completely different from melee, but with its great shield pressure for above platforms and its very short landing lag it is still very solid. nair-> fast ground move (usually jab) works very well. Dair is very nerfed compared to melee, considering it no longer spikes with the weak hit box and the greatly increased start up lag. Not useless, but very situational now. His Bair is no longer a sex kick, which is disappointing but it is very quick and hard to punish, it also has impressive kill potential for its speed and range. Up air is pretty much the same as in melee, very solid. Fair is completely different from melee, it is mostly used for gimping because its multihit lasts forever, has a great hitbox, and either the last hit doesn't connect and the opponent is stuck at falco's fast fall speed below the stage or the last hit does connect which has a great angle for gimping.
IMO falco's bread and butter are: Jab, f-tilt, up-tilt, up-smash, bair, nair, side-b.
moves with a niche use that they do very well: d-tilt, f-smash, d-smash, fair, u-air, shine
moves that are generally not very good but may be useful in the right situation: laser, up-b, d-air
That should cover everything,
Hope this helps :D