PS Vita by far

I go with 3DS, particularly XL version has a very nice big screen and it's also extremely comfortable to play with.

I own GBA, DS, 3DS, PSP and PSVita.

Out of these systems, my favourite one would be the 3DS, since it's basically a DS stripped of it's GBA compatibilty. And since I currently consider 3DS's software library to be superior to GBA's (even though it is close), 3DS takes the cake over the DS.
That said, I love every handheld I owned so far. The GBA is an amazing system all on it's own (and actually my first console ever), only made better by that fact that it plays every Nintendo handheld game released before it.
The PSP probably offers the best value out of every system that you could buy at the moment. Not only is it itself fairly cheap (allthough I'd rather get a 3000 series used than buy the abomination that is the E1000 series), but the games are cheap, too. I have about 40 PSP games in my possession, and the most expensive game was Valkyria Chronicles 3 E2, which I had to import from Japan, and cost me 35€. The price of my PSP library averages out at 10€/game.
The Vita, although often overlooked, has taken a special place in my heart, too, and in some way manifests the gaming taste I have acquired over the years, which went from Pokémon and my favourite game of all time, Paper Mario 2, over the Fire Emblem series (my favourite series of all time) to a broader enjoyment of JRPGs and Japanese niche games in general. And there's plenty of them on the Vita, so I can't exactly complain.

And while I was writing the bit about the Vita, it came to me that 3DS does have region lock, so I might put the DS top, since, again the only difference in their game libraries is the difference between GBA/3DS games. It's really hard to name one of these systems your favourite when you think that they are all amazing. Although I can definitely say that I enjoy my Nintendo handhelds more than the Sony ones.

Nintendo DSi, best game library ever, PS Vita second place.

Easily the GBA. It has many awesome original games like Superstar Saga, Metroid Fusion, Aria of Sorrow, Minish Cap, Advance Wars, but also many awesome remakes like Pokemon FireRed, the Mario Advance games and Metroid Zero Mission.

My ranking:

• 1: PS Vita
• 2: iPad  (point&click adventures are my favorite genre)
• 3: 3DS XL  (sooo much better than the smaller 3DS)
• 4: PSP
• 5: DS lite  (the last DS-model with GBA compatibility)
• 6: GBA
• 7: 3DS
• 8: Gameboy Color
• 9: Android devices (a less clunky and heavy "Nvidia Shield 2" with Tegra-K1 and better software support could climb some positions)

So far PSP. No contest.

But if, for whatever reason, Vita gets the software it desrves, I might change opinion.

Only six percent for PSP? Son, I am disappoint.

Vita cause it's my first handheld :P Only the Plus made me buy one and so far so good. love the games but more support would be awesome though I doubt we'll see many more AAA games. But I'll play every single one that interests me

3DS. It is a crime that this system isn't the best selling handheld system ever. I feel like if it had been released instead of the original DS, it would have at least beaten the Gameboy in sales. The price is good, the games are the best any handheld system has ever had even with subpar 3rd party support, and the features are amazing. My only complaint is how tragically underutilized some of its features are, like the augmented reality stuff for example.

Second place goes to GBA, specifically the SP model. That backlit screen changed everything for me. But it was the first time I felt like portable games gave me a really deep engaging experience. Original Gameboy/GBC had its moments but was mostly only successful for offering decent gameplay for an exceptional price. GBA maintained a fantastic price while offering deep gameplay experiences.

Third place is tough. I want to give it to DS, because I do think the system was innovative, and certainly we see its influence everywhere. It had good game variety, but in my opinion most of its games were less polished than I'm accustomed to. It was a time where developers, including Nintendo, were figuring out how to make good games for a touchscreen input, so its forgivable, but those Zelda games, damn, those Zelda games. They were the worst in the series. I'd rather play Four Swords Adventures than Phantom Hourglass and Spirit Tracks. Metroid Prime Hunters was okay, but lackluster in comparison to any other game in the series. Mario and Luigi Partners in Time was the most mediocre in the series, Star Fox Command was just bad as much as it pains me to say it, and Pokemon, well, Pokemon left me uninterested in the series for two generations straight. PSP was much less innovative, but it had absolutely superb support with its games, so I say it actually ties with DS.

4th I say is a tie between Gameboy and Vita, because Vita has a lot of innovative moments but Gameboy gets respect for its variety, unmatched price value, and impressive legacy. Vita has the potential to rise above it if it starts getting more than just anime games, indie games, and niche Japanese genres.

After that, Game Gear had some good games, but its design was unforgivable. 5th place. Not much else is worth mentioning. The tablet and phone games are an abomination to the industry, not because good games can't be made for them, but for the damaged they've cause with their bottomless mire of horrifically bad games. Last time we had such a slew of bad games it largely contributed to the crash of the industry. As for Open Pandora, I've never heard of it, but it sounds like it's in a league of its own as the ultimate emulator, so it definitely deserves respect. Props to OP for introducing me to it. I can definitely relate to the OP, as I also have been doing portable gaming by orders of magnitude greater than my console gaming.