Without a doubt, the SHIELD TV.
It's the most powerful ARM device on the market and it will run everything you throw at it.
From fullspeed Sega Saturn emulation in FullHD, to Dolphin emulation (the only ARM device to run Dolphin well),
this thing is a beast.
The only downside is that it costs 199$ but if money is not an issue, get it.
The Raspberry Pi 3 isn't very powerful in comparison and it is currently not able to run Dolphin
due to the 32-bits design in the GPU so the OS remains 32-bits, even though it's a 64-bits CPU.
(This will soon be figured out in upstream tho, i hope)
It should be able on the hand to run PPSSPP, Reicast and uoYabause at native resolution with little issues tho,
if you are really careful.
The only PS2 emulator for ARM devices, Play!, does not run very well even on the SHIELD.
If you really want PS2 emulation, you might consider building your own ITX x86 box.