Honestly, I just think the 3DS is a bit too bulky. The PSP would be nice, but...I would want to modify it a lot to make it not look like a Sony device.
Not exactly sure what you have against Sony devices (a logo is just a logo), but I do see what you mean about the 3DS being a tad bulky, though.
Ultimately, it comes up to preference. All devices can emulate the NES, SNES, and Genesis fairly well, so if you only care about those games, then just go with whatever you feel like. I feel that the PSP/PS Vita has an edge over the 3DS in terms of emulation (thanks to semi-native PS1 support and to the MIPS architecture making N64 emulation feasible at all, in addition to better GBA Emulattion support), but the 3DS certainly isn't a bad emulation device, and is still able to play a wide variety of games from all sorts of devices.
Another thing you should probably keep in mind is that each system I listed above has it's own set of games. Depending on your taste, you may find yourself leaning towards the 3DS's library, or towards the PSP/PS Vita's library.
You could, as
@DKB pointed out, just 3D Print a case and wire together a Raspberry Pi with a screen, then load RetroPie and all your ROMs onto an SD Card. I'd recommend the Raspberry Pi 3 for this; that little sucker can emulate systems all the way up to the Dreamcast and PSP. Going this route requires that you have some knowledge about soldering and at least some basic experience with Linux, FTP Servers, etc., etc.
You could also just get something along the lines of a
GPD XD. It runs on Android and, thus, can use all Android emulators. You can even play some nice Android ports of older titles on it (Sonic 1, 2, CD, and Crazy Taxi come to mind).
The answer isn't as simple as it seems. You kind of have to weigh these strengths and weaknesses when picking your handheld.
