Indeed, I actually think Tetris and Puyo don't have too much in common except the obvious "drop puzzle" genre. They have a really different feel - Tetris is faster, more primal and minimalist, whereas Puyo feels more elaborate, with a higher learning curve and a distinct method of attack and defense.
Like one of the guys in the recent 8-4 podcast said, it feels like those two games hit different parts of the brain. I initially didn't like that I have to consciously think ahead more in Puyo, but with enough practice you can really seek your brain learning patterns and executing them almost reflexively.
After an certain point, Tetris feels like it is "just" about speed, consistency and execution, whereas I still learn new approaches and strategies in Puyo. Still, Tetris has a legendary status of intuitiveness that will probably never be surpassed.
Yeah it seems like there's a lot more possibilities for interaction between players in puyo due to how garbage drops and is cleared. Seems more interesting as a versus game than Tetris.