I was going to write a part about how a real vs. puzzle game is nearly impossible due to lack of direct player interaction... but then you went and edited that in. Tetris has always been the worst about that though IMO -- it feels like whoever has the higher APM and cleaner builds wins 95%+ of the time. Lesser skilled players have no shot unless you're playing some weird variant, and the game ends up about as interactive as a versus game of Beatmania IIDX. (As an aside: high-level Tetris w/ Card Captor Sakura is hilarious because specials are going off every 2-3 seconds -- it's MvC3 levels of spastic at times. But that just makes things for the slower players worse...)
At least in Puyo you have some decisions to make in regards to cutting a chain short, and players being attacked can keep building out during the chain and counter with something bigger. That leads to its own problems, though. I always thought Puyo would have been better if a counters led to a soft reset of the chain, so that a 10 chain clearing an 8 chain would lead to a 2 chain's amount of garbage being sent over, not the 9th and 10th parts of the chain's garbage... but what do I know, I'm a scrub at that game.