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.
Actually, Sakura Tetris uses the system I described(game is derived from TGM2 with some input tweaks). If you watch closely, you'll notice that garbage is NOT random. It is entirely determined by the actions of the other player, and is simply a height-inverted version of the material that was there before the clearing piece. This means that each player has direct influence on the other person's stack, and makes it an actual VS environment. Of course, this also means that clearing 2, 3, and 4 lines sends 2, 3, and 4 lines respectively instead of 1, 2, and 4 like in guideline Tetris. There is NO special bonus for T-Spin clears, as t-spins are just one of many kind of spins you'll have to do in an ARS game.
A key subtlety of the item system in Sakura Tetris is that NONE of them add to your stack height, except possibly for that weak item that adds single blocks randomly. What they do is various sorts of reconfiguration on what already exists on your stack, so
the higher you've built the more vulnerable you are. A perfect example is the lightning bolt, which clears a single vertical line at random. If you have like 2-3 lines of material on your screen, this is almost a non-issue, but if you have 15-17 lines of material, you're fucked. Even the most powerful item, Eriol's Stack Invert, only takes effect to the highest row a piece is present.
Speaking of which, each character determines the specific effect of each colored item, and because of this and the fact that both players are working off the same piece distribution there are matchups, and because there are matchups there is also a tier list. Eriol is S tier, Sakura (regular) is A tier, and Kero is bottom tier. I usually let the people I play pick Eriol. Anyway, I don't see what the problem is with rewarding fast play, as that's what Tetris is all about in the first place. The faster you play, the more quickly you can clear your screen and the more quickly you can set up garbage for the other side. In Sakura Tetris, you're given an item piece at a regular interval of pieces used, so you also get items more rapidly this way. At the same time, the greedier you become the more you expose yourself to attack, and since you also get stack clearing items a less experienced player can stick around a lot longer. All that said, the spawn delay in Sakura VS is pretty slow regardless, so you really can't get things as fast as you can in TGM VS.