I have played lots of puzzle games, but I disagree with WindRider's big wall of text. I think that tetris attack is great if not greatest puzzle games, but VS mode has problems.
I agree that Tetris Attack has less luck than other puzzle games, because you get to see the entire stack to plan and make your future moves. You, however, have to be careful when counting moves in piece placement puzzle games like Tetris and Puyo, since good players think in terms of several pieces(since you can see the next pieces) and those pieces can be dropped really fast. Expert players arrange their stack in those games to maximize their chances when getting any random piece. Also modern Tetris variants have a randomizer that is not as random as older Tetris games.
Tetris Attack isn't as aggressive as it implies because attacks don't matter, the only thing that matters is that you don't miss a garbage chain which isn't very hard... This leads to matches that are boring, and overly long. There is a lot more skill and variety involved in regular chains than garbage chaining... This sentiment is shared by a bunch of players on http://www.tetrisattack.net not just me.
In fact, I am learning puyo because it is IMO a better VS game. Since a 3x cancels a 3x you can say that the same skill level cancels each other out. VS mode in tetris attack doesn't reward the skill required to constantly make 13x chains; slow garbage chaining is all that matters. In Puyo's VS mode the skill required to make huge chains is rewarded appropriately unlike Tetris Attack's VS mode.
You have to remember you can't compare Wins to Loses in games direcly since the longer a round is the less that luck comes to play. One tetris attack match that lasts 5 minutes should be compared to a set of puyo matches that are 5 minutes long. Also good players can sometimes dig through garbage in puyo, and use it for chains. Another trick is raising part of the stack so that when garbage falls a part of the chain is still accesible through the sides. If one player is completely filled on top with garbage then they will lose very quickly. Also players know when they are dead, so they may give up. The game isn't in the state where one player is playing defensively for long.
Puyo Puyo ends without warning in a single attack that may not even be that impressive.
When a chain goes off there is a sound... The context of an attack is very important as well. Players look at their opponent and do a 2x power chain (a big 2x combo in tetris attack speak) when they see that their opponent can't counter it. Here are some movies of puyo experts btw:
http://www.youtube.com/results?search_query=puyo+import&search_type=&aq=f