Falco's is better for Sheik because it lets you combo into her U-smash easily and that's ridiculous. Shine to Dair/Uair/U-tilt would also be stupid for combos. And it allows her to just hit Shines vs space animals for combo starting and continuing so tech chasing would be largely obsoleted in favour of automatic death combos.
Ironically enough, tech chasing would also be made more powerful because you could Shine the tech stand/non-tech and get a huge auto-combo and dash attack/boost grab the rolls.
For frame advantage Falco's Shine is strictly superior to Fox's. Sheik's Multishine with it (she has the same jump speed class as Fox) would be absurdly good. Probably too hard to execute to be a real strategy, but Shining twice then wavelanding off a platform seems like a good way to attack a shield on most levels. Sheik has some notoriously good grabs, too, so Shine grab from her (with all that juicy frame advantage) would be a really good option.
Her edgeguarding is fine she doesn't need Fox's shine for that since her weak bair --> another bair --> edgehog is already as lethal as a shine spike vs space animals and she can strong Bair or needle or whatever anyone else. Fox's shine might setup tech chase onstage but Falco's straight up combos and guarantees a follow, which you can then use to setup a tech chase or make a big combo, so the consistency is better.
Anyway enough stupid theory.
Let's talk about the Ice Climber matchup. Or unique spots to use needles in edgeguarding. Or something.
It's so dead in here.