I own both iD L and P's, but I really, really want a TMGC+C ;3;
P's is quite overrated; it's not that great compared to the iD L unless you're going to buy pierces as well. And they usually cost $10 at the minimum.
The iD L has more total characters. The P's has the same number of adults, but only two babies instead of four, four toddlers instead of six, and four teens instead of six. I think P's has better built-in games than the iD L, but they last longer than the iD L games.
The P's has REALLY nice built-in room themes, better than the iD L backgrounds in my opinion. You can add color schemes to toddler and teen characters but there aren't that many color schemes and they don't look very good You can take your Tamagotchi to school and work, which has really cute animations.
iD L has a feature where you can grow plants to get new items and food; a great feature that was sadly removed from the P's. ID L has Henshin Jo; you need to buy pierces if you want to transform your characters on the P's. I also miss the TamaTama market (but you can still sell your stuff to characters outside, it just seemed more convenient at the park XD). The P's easily gets dust and hair under its faceplate no matter how hard you try to protect it. And one last thing about the P's is that it takes more effort to change the time, sound, contrast, etc. You need to go to a certain option under the stat menu to change them and you can easily forget which option is which if you don't know Japanese.
Both versions have their pros and cons and although I prefer my iD L, you can decide which is best to your liking