Brawl's single player is not better than Melee's. Okay, I'll give it Subspace Emissary over Adventure (though even that's debatable - Adventure is more replayable and has arguably better fanservice). But while Brawl has more content, almost every mode that's in both games is better in Melee. And why are people acting like Melee was bare-bones on content? On its release it was praised for the plethora of different modes and things to do. Yes, it's multiplayer first, but there's more single player than most fighting games.
In Melee, the character lineups for Classic and All-star were random. You would fight characters in a different order every time, which gave it replay value. You have a mostly-fixed character/stage order for Classic - you'll fight a Zelda character for the first match every single time, while in Melee you might not fight one at all. The type of battle (team, giant, single, etc.) is randomized in Brawl, but it's still not as good as a different order of characters every time. It makes it less fun to replay. Reverting back to a fixed character order like Smash 64 (which Melee was praised for fixing) was a bad idea.
All-star's order is even more rigid, and the difficulty progression from Melee (from solo to doubles to triple opponents) is gutted. Both classic and all-star also lack the scoring system - earning little achievement-type bonuses was fun and a feature of Smash since 64.
Break the Targets is completely ruined with five bland stages instead of one tailored for each character. Home-run contest fares somewhat better, but the addition of the shield around the platform takes away from its uniqueness and challenge.
Multi-man Melee - Okay, this is pretty much the same in both games.
Trophies - Brawl has more. But Melee has a better selection. Brawl's are heavily weighted toward recent games and have way too many bland Subspace villains that are tedious to get. And Melee's are more fun to earn, really one of the best "achievement" systems ever. I enjoyed getting them in Melee, while in Brawl I got bored long before. Beating Adventure with every character could get old in Melee, but Brawl has a lot of tedious trophies that are worse than that, especially since a lot of the single player modes are worse than Melee. I would prefer them not to do trophies in Smash 4 unless they can think of a way to make them really fresh and different.
Brawl does have boss rush, but it's not really that great. The game's mechanics aren't designed for these types of bosses. Master Hand was fun, but fighting a bunch of Master-Hand type enemies in a row gets old.
Events are better in Melee. Admittedly, I didn't play the co-op ones in Brawl. But Melee's are more creative and change up the rules more often.