I seriously don't get why Adventure Mode is so liked, especially more than SSE.
It's the definition of half-baked, for me. You got three neat side-scrolling levels, but then it basically abandons that in favor of more or less Event Matches. And it's the same thing, and you have to do it with every character. It got stale.
SSE was way better, imo. It wasn't perfect, but it was way more varied, and was a fun way to unlock everyone if you enjoy the SP-style of Smash. And people, when Brawl came out, acted like it seriously detracted a ton from the rest of the game, but Brawl was about equal to 4 in terms of the main content, and 4 doesn't have anything near SSE-levels.
I didn't like SSE because they purposefully changed the
physics of the characters, making them feel entirely different and control entirely different from the multiplayer. They run slower, they are even
floatier (which makes them more prone to getting launched by enemies everywhere), and other miscellaneous attributes were changed about them. The changes make SSE play worse overall and it really impacted my enjoyment of the single player in that respect.
But not only that they also had you fighting enemies that were basically sponges and weren't very interesting to look at let alone fun to fight. It's literally a Kirby game through and through and I didn't like it because... well, in Kirby games you can suck up enemies to get powers to KO them more easily -- in Smash.... that's not there at all. And if you want to get that kind of experience, you're forced to use the half-baked sticker "equipment" system, which by the way, the game doesn't even really introduce you to it let alone tell you about it when it becomes meaningful to use.
THEN the level design of SSE itself is... not fun it's a chore to slog through. You do some mediocre platforming, eventually are forced into a fight with SSE enemies that you have to clear, then you can start moving again where you're going through yet another boring platforming section (and hell it may not even be platforming, it may just be running in a straight line). And then of course the fact that SSE levels themselves drag on for what seems like eternity, too... and there's
a lot of them as well. All with the same general formula. It's a drag.
Melee's Adventure Mode is well liked because
it is short and changes things up on you. It's not just mediocre platforming -- in fact, even the levels that are focused on that the characters feel the
exact same as they do in multiplayer, their physics are unaltered. So you can blitz through the Mute City speedrun level with Captain Falcon at the same running speed as in multiplayer and it's
fun as hell (and actually was challenging the first couple of times with some characters). You're not inhibited at all by the game. And it also helps that those levels have the Nintendo aesthetic where it's clear time and care were put into it, making them very memorable.
I liked how it had a few special matches intermixed with the platforming levels, it made it feel like... how a Smash single player mode should be. It didn't get boring to me to do it with every character, either (then again Melee had a smaller roster so doing it 26 times is less of a slog than doing it 51 times... lol...). To me, it's better than SSE because it's more replayable than SSE was and that's what matters more: replayability. That's what all of Smash's single player modes are like (save for Event mode where you play the events once to beat them and then never again unless you wanna get a better time) they are made for replayability so you can play them in under a half an hour or so to unlock stuff, get rewards, and then go back in and do it again if you want.
How replayable something is just depends on your tastes. I quite enjoyed Melee's Adventure Mode enough to do it a gazillion times even after I beat it once with every character. It never really got old to me. Meanwhile in Smash 4 All-Star Mode is... way past old to me right now because it's literally the same thing every time, nothing changes -- at least in Melee's Adventure Mode where the Triforce was in the maze was different and you could alter some of the matches you had to play and etc etc. Small differences like that made it different enough.
That's just what I think, though. I'd take a handful of shorter platforming levels (like 10 or so) ala Melee Adventure Mode based on Nintendo franchises mixed in with some traditional albeit specially made for matches in an Adventure Mode over the gargantuan 10-hour borefest that was SSE.
Edit: Oh and Melee Adventure Mode gave us Giga Bowser, that's another reason to like it more than SSE. Sure Event Match 51 existed but he originates primarily from Adventure Mode if you do it on... Hard or Very Hard iirc.