I played this game like mad back in elementary school and college (yes, there was a decade gap where I forgot about it). I never was a master like you can see in some youtube videos, but my roommate and I got good in our own respects.
Planet Puzzle League is the only "real" way to play online, and I did that whenever the game came out but it's not the same as Tetris Attack.
My roommate and I were very nitpicky about EVERY version of the game and we tried them all. Panel De Pon for the Super Famicom, Tetris Attack, Pokemon Puzzle League, GBA Puzzle League, and Planet Puzzle League. All are different in two important area you might overlook: how long can you stay at the top before you die (PdP = not at all, Pokemon = forever), and how long do you have to slide blocks over before a layer or block drops.
We found the original Tetris Attack to be the best version, although PdP was sometimes better if we wanted quicker games (you die quicker).
Planet Puzzle League for DS, even on the harder difficulty, still gives you a bit more time than Tetris Attack. The problem is that stylus control is TOO GOOD, and the games last a long time and is just non-stop giant chain vs giant chain. Tetris Attack is more about fast 4/5 sets and 1-3 chains rather than the giant attacks, and we liked that.
Just wanted to ramble.
edit:
Here's the strategy I like. Once you have a few gray blocks available, throw down as big of a regular chain you can muster. Then immediately use all of your gray blocks. Finally, spam 4/5 sets and quick chains as fast as possible. Gray blocks interrupt your opponent's breaking up of your offensive garbage. So by the time he has cleared both your big chain and gray blocks, you should have a good array of quick dissolving 4/5 sets and small chains that do not give him much time or space to prepare for.