My vote is for the 3DS despite it selling the lowest.

The GBA was a phenomenal handheld for the cheapest entry point the industry has ever seen on a mainline console when you take inflation into account. It coasted the success of the OG GameBoy and of Pokemon. It had a good library despite the fact that it was ended too quickly. It was sacrificed for its successor.

The PSP was an amazing machine for the time and price that had great 3rd party content. It came on when Sony was dominating the console space and it failed to replicate the success due to the enormous success of the DS that caught the industry off guard.

The 3DS was not as cheap as a GBA and was not as powerful as the PSP when you adjust it for year of release. It also had the toughest job and was in the least privileged position. It had to save Nintendo in a moment where their consoles failed and where smartphones were set to destroy the handheld market. It succeeded.

It put Nintendo in a position to try to move to the hybrid and the rest is history and it did on the back of amazing games. The 3DS saved handheld gaming, saved Nintendo and must be respected for what it has done. It demolished Vita, was able to stand against the wave of the Iphone and was able to pass the torch to the Switch. A very underrated console for its feats.

I can't pick definitely one of the three.
Every system is unique, but for sales standards, PSP won definitely.
GBA and 3DS is quite close both to Sony's second handheld.

I just can never take statements like this seriously from Nintendo fans. Sorry.

I mean I have more nostalgia for the GBA and admittedly more playtime on it, but as for which system is best... yeah it's probably the 3DS, zelda remakes and some other seriously good games on there. GBA is mostly carried by a very good Pokémon generation.

3DS because of its game catalog, it has way more memorable games than gba, which was basically a Pokémon Machine.
I admit i love 3D Land.
As a hardaware the answer is obviously Psp, unless every 3ds had an ips screen...

3Ds also had many  themed variants which were masterpieces , but also been the butter of scalpers bread. 

I liked 3DS way-way more than GBA. Didn’t play PSP, so I have no opinion on that one.

I found the 3DS had a significantly stronger lineup: Xenoblade Chronicles, Monster Hunter Games (including 3 and 4 as an exclusive, and Generations), Sega 3D Classics, Super Mario Kart 7, Animal Crossing New Leaf, A Link Between Worlds, several Fire Emblem games (Awakening, Revelation, Conquest, Birthright, and Echoes), several N64 games 3D remasters (including Lylat Wars, Ocarina, Majora), Super Mario 3D Land, Kid Icarus Uprising, Radiant Historia,  the series of street pass games, glasses free 3D, the 3DS virtual console, the ambassador free games for early adopters, the entire DS library because of backward compatibility.

My main memory of GBA is the lack of a backlight while playing Castlevania Circle of the Moon in direct sunlight (because the game was so dark that it was not very visible otherwise), Fire Emblem Advance and mainly playing it on DS (because of the better screen, with lighting) and very buggy FF ports: although I enjoyed the FF4 post game extras… but again, played these on DS, not GBA. Also, backwards compatible DS was available in the middle of the GBA’s lifespan, and its backlight made the GBA obsolete.