Neither emulate Amiga properly. Amiga on PSP reminds me of WinUAE in late 90s and that's no better than a system that doesn't emulate Amiga at all (DS).
PSP emulates CPS1 & CPS2, 16 bit consoles including SegaCD very well and is a better choice for emulation however DS has a surprisingly good NEO GEO emulator.
PSP has some interesting titles like Patapon but they're too few to matter. I often find myself using emulators on it but I still play my DS for great titles like Henry Hatsworth, Fire Emblem, Advance Wars, Ace Attorney and Professor Layton series.
In short, get both if you can. If not, go for PSP for emulation and DS for some native gems.
And if you decide to get a DS stay away from any pirate card with "r4" in its name. The original r4 was a great card back in the day but it's dead now and the name is used by irrelavant 3rd party crap. Get a Supercard Dstwo instead (Acekard Ak2i is the second best imo)
As for PSP, get a sony memory stick to microsd converter so that you don't have to use their propriatery shit.