Puzzle games is an odd one, in that there were loads on both but the nature of the DS was perfect for it, Layton was a huge deal and that's four on its own. Puzzle Quest was on both, but PQ2 and Galactrix were cancelled on PSP. Might & Magic: Clash of Heroes was amazing, one of the best titles on the DS, and Meteos was great too.
Admittedly it's been so long that it's not like I have an encyclopaedic knowledge of them!
I also think it's a bit unfair to count a single collection of Castlevania games as somehow a win in the genre for the PSP here. The DS had three original games, Order of Ecclesia and Dawn of Sorrow are both great games, with OOE regularly placing highly on series lists these days, and there were others in the genre too.
What about Zelda, Okamiden, Solatorobo etc? Do they technically count as '3D action adventure', they've always seemed like their own thing to me.
Some others in favour of the PSP though: I remember playing some scrolling shooters on the PSP like Darius that were great too.
Also- Monhun is pretty much it's own genre, seems like the elephant in the room here, not like DS could compete with that.
Ultimately it comes down to what genres you prefer. I've always preferred slower, turn-based and 2D games so Layton, Hotel Dusk, Phoenix Wright and Etrian Odyssey made up a ton of my time on DS, whereas the PSP felt more like a cut-down PS2 with a range of games to match. Great systems.