But, if you can only pick ONE company then i suppose you're picking it because of their OFFICIAL support/advantages.
Then choosing Sony because PSP's were an emulation powerhourse seems a bit silly, What were the official games anyway? I remember my PSP having NEOGEO, TURBOGX folders, but never saw any of those on psp's official format. Without homebrew you would only get PSP/PSX, correct me if i'm wrong please, i'm puzzled.
The 3ds has VC for GBA (ambassador), NES, GBC, GB and SNES (n3ds only), so that would have more official emulators than the PSP.
I can't really decide, I've had a PSX, PS2, DS, PSP, 3DS, Wii and Vita during my lifetime. I just don't know what criteria to use and judge.
Variety in genre's of games?
Comfort-ability in controls?
How long games are in average for the console?
If the game's are aimed at adults, childs, etc?
What i played the most in my lifetime was on my old PS2 (RIP), but my former DSlite and current PSP equal in a close second, 3DS being third.
For the wii and Vita i've them since November and December respectively to be able to judge. Haven't had time to give a full play to a game of those consoles yet.
Never had an Xbox/360/ONE or a gaming PC (having a coffee maker that barely ran psx and DS back in the day doesn't count).
EDIT: If apple's an option shouldn't android be it as well? Both are considered gaming oriented devices if you pick the proper-not-freemium games.