Normally, I'd say the Nintendo handheld is always the best one, but these two are not in the same generation. I'd have to give it to PSP this time. 3DS is the worst Nintendo handheld I've played. It really does not have many games that I want to play. I really liked Theatrhythm Final Fantasy and also Fantasy Life. I had some good fun with Bravely Default, but I felt the game was padded so I quit around 1/2-2/3 of the way in. I tried several other 3DS games, but they really aren't that great. Most Nintendo first party games I would prefer to play on a home system. I don't want to play Mario Kart, Smash Bros, Hyrule Warriors, etc... on the 3DS because there are home versions of those games I like better. Also I seem to like Fire Emblem a lot more when it is on a big screen. I just have never enjoyed Fire Emblem on a small screen too much. I've never been into Pokemon and the rest of the library is kinda...meh.
Meanwhile, PSP had several games I really enjoyed like Crisis Core: FF7, Dissidia, Patapon, and Final Fantasy Tactics. It also has several games I feel like I missed the first time around like Tactics Ogre, Jeanne D'arc, Trails in the Sky, etc... basically a lot of RPGs and Tactical RPGs. The battery in my PSP is currently dead, but at some point I know I'm going to buy a new battery, dust it off, and then play a bunch of PSP games I've never tried before. I don't think I'm ever going to do that with my 3DS except to play DS games. Also the PSP can be played on a home TV and that is a feature I really like.
PSP really is the better system this time.