Brawl is much larger, that is pretty much the only unbiased thing you can say. As for the actual gameplay it really depends on the person and which character you use.
To me one of PSASBR's biggest accomplishments is the diverse roster. No character is a clone. What this means is some characters play like Smash while others are so far out there they feel alien. Drake is a great example of this because a match of four Nathans is as far from Smash as you can get. Meanwhile a match of four Heihachis is on the other end of the spectrum and is very close to traditional fighters. In between characters like Sweet Tooth replicate Smash's fighting, ignoring the differences in metagames of course.
This is also why many people think the roster is unbalanced. The characters are just like a rock paper scissors game in 1v1 matches. Heihachi beats Sweet Tooth, Sweet Tooth beats Drake, and Drake beats Heihachi. This is why the game really shines with free for all matches and 2v2.
As far as the metagames go, both Smash and All Stars are fantastic. The problem for PSASBR though is it sounds bad on paper. "Supers are the only way to kill and attacks don't do damage? F that!" After playing however most people start to understand the magic. One thing in particular that I find fantastic is how each super level takes more and more AP to reach. What this means is if a player is close to a level two, they can preform three level ones in a row back to back. Without playing you can't fully understand why this is great, but long story short it allows you to see when a player is desperate.
So Brawl is steak while PlayStation All Stars Battle Royale is lobster. Personally I'm in the mood for seafood right now, but man do I also crave a prime rib.