TTYD's gameplay is vastly improved over its predecessor in both the main game and when it comes to optional things to do.

Paper Mario treated you like a baby in the beginning and it would take quite a long time until the action commands unlocked. TTYD on the other hand had them right from the start, plus the ability to counter enemy attacks, giving the battle system another layer. Another major change was the ability to switch the position of Mario and his partner and both having an individual set of HPs. In Paper Mario, enemies would rarely attack your partner and if they did, the partner was forced to sit out for a number of turns. In TTYD, it opens up a lot of strategies because the character in front will be the primary target of attacks. Likewise, the badge system now also covers a wide range of partner badges, adding even more depth and options to the battle system.

A lot of star pieces in PM had to be won by answering questions correctly and the quiz was annoying to trigger. It doesn't hurt one bit that this was removed from the TTYD which featured a similar number of non-quiz star pieces. TTYD integrated sidequests where PM really had none. TTYD also featured various lists that motivated completionists to scan all enemies, collect all badges and cook all recipes. There was just more to do in the GC game.

What argument do you have in favor of Paper Mario other than it being a game of your childhood? TTYD is better in every aspect, although admittedly many parts of it are a remix of elements found in PM.