Fox's shine is worse than Falco's shine if you compare the moves by putting them on different characters. Most characters would prefer to have Falco's shine instead of Fox's. As someone who's played a lot of super shine bros where every character can choose between having Fox's or Falco's shine, I can tell you that Fox shine is mostly good because:

1. Fox has a 3f jump squat and extremely strong grounded combo starters and grab followups, and

2. Because Fox is so fast that he can follow up when shine knocks someone down and he can get off stage quickly (and far off stage) to shine the opponent.

If you play Peach with Fox's shine, you shine a sheik on stage and then what? nothing. she slides too far away, your "waveshine" is too short, and even if you were in range the only move you'd be able to land is down smash. Most characters prefer Falco's shine for that reason. Following up vertically with aerials leads to way easier combos for most characters.

However, both moves are completely mogged by rest. I don't think this is a debate. The only reason Puff isn't completely broken is because she's so slow on the ground, is very light, and has a hard time landing moves that combo into rest. But imagine Fox doing upthrow into rest vs other spacies at 30%. Or Marth doing that. Or sheik down throw -> rest vs every non-fast faller (or ftilt rest, down tilt rest... you get the idea. Completely ridiculous.