Honestly it's a difficult question, there are many things that make me like one hardware over the other even without touching the availability of certain games. My list would probably be:
The PSP just spat out good game after good game, it was a like a AAA-Title Machine Gun.
Don't get me wrong, I had an awesome time on my DS, but for every game I played on the DS, I played a game on the PSP that was better.
Legend of Zelda: Phantom Hourglass, Four Swords, etc. Got beat out by games like FF: War of the Lions, Kingdom Hearts: Birth by Sleep.
Super Mario Bros? Answer it with Metal Gear Solid: Peace Walker.
Mario Kart on the DS were some of the worst Mario Kart's imo.
I do think (without even owning one) that the 3DS has the ultimate handheld games out of them all though.
However, everyone has their own opinion.
I just personally believe that the PSP was more comfortable, was more powerful, and had the better games.
Now, don't get me wrong 358/2 Days on the DS was good, but BBS on the PSP blew it out of the water. Better Combat, Better Music, Better Characters and even better cameos.
I beat Peace Walker. It was good just not Mario good. Tried KH and didn't enjoy it. Didn't even bother with the FF game as I'm not a big fan of those games.
Are we judging these systems relative to their own time period, or just ranking them in the current landscape? If it's the latter, things like backwards compatibility makes some of these systems obsolete (3DS vs DS).
Crash Bandicoot and a lot of PS1 games have yet to be on the Vita store.
Along with games such as Final Fantasy: VII Crisis Core, Final Fantasy 012 Dissidia Duodecim (It was on the store, but was removed for unknown reasons).
Plus Birth by Sleep hasn't made its way onto the Vita, nor has Phantasy Star Portable, some of the Dynasty Warrior games.
There are tons of fantastic PSP and PS1 games that may not ever see the light of day on the vita store.
Plus, if you are up to date on your PS Vita updates (no pun intended), ROM hacks are out of the question.