Lumines 
Tetris Overall Comparison For some reason, I just love Lumines. It might be one of my favorite falling block puzzle games. Not that there are many of those anyway =P
With Tetris, I always tend to paint myself in a corner by having a tall empty space on the side and then messing up the pieces in the middle. Whenever that happens, it's kinda annoying to try and recover from it. With Lumines, if I make a mistake, I feel like there was more I could do to recover and keep playing.
Cool part about Lumines is that there is a mode where you battle against various computer characters. They can get really hard, but it's rewarding once you beat them.
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CommandantCommandant Level 9
Comments
I'm going to agree, though this is a close one. I never played Lumines on PSP however I did play it on Gamegear...remember that ol' piece of machinery. It was the best handheld since Lynx.
Lumines has a cooler feel than Tetris. Its kind of like Tetris evolved, with a cool modern spin. I give it to Lumines, though you got to give the icon Tetris its due.