i'd personally choose PSP for things like NES/ GBC/GB if we're going apples to oranges here. emulators (gpSP and Homer's Rin are more refined and compatible compared not to say they arent w/o issues) but the DS cant be beat for SNES emulation either by Virtual Console or by things like the snes9x port which orginally was ment as an answer to Snes VC on the O3DS. my reasoning for that is Snes9x TL for the PSP has too many flaws and inaccuracies, where Earthbound runs fine in Snes9x on the 3DS and no issue at all in a N3DS offical VC. the PSP 's emulator however, its bad enough that it triggers earthbound's Copy Protection (increased enemy spawn/higher levels and if you make it to giygas, well the meme of your XXX (whatever here) is just another meal to him!", well your Save file was just another meal (it triggers the crash and save wipe final check at that fight.)
one System you cannot beat the PSP at however is PS1, its a core part of the PSP and for a handfull of games its just a matter of using POPSloader and selecting the right POPS version to make work or changing to the right Game ID (i know you neede dto change ID and use a specific pops version for Chrono Cross *Before* square enix finally released a "Fixed" official port
if your investing alot of time into GBA i dont know whats better, gpSP on the PSP (has plenty high enough compatibility even cheat support) or the 3DS's VC (albeit you need the right set of patches for some games and some need manual Hex editing of the rom before hand,) the few actual needs for a better emulator that 3DS's VC cant provide compatibility for, you need SNES games or dont care about PS1 games, that one could argue you could be better off soly sinking mainly into an N3DS for emulation.
edit: if you want to get a Switch for much more in emulation than what the 3DS and PSP are limited to , your going to want to do it soon before Mariko units appear in the wild. which may/maynot likely need an actual soldered on ship rather than how we can abuse by using RCM with current units. go for whats easier for your terms in the long run and easier on your wallet. a PSP is the cheapest if you get a older PSP2k then a N3DS + NTRBoot compatible/preflashed flashcart second cheapest then a switch at near 300USD
its literally the same chip, it even uses the same arm7 coprocessor, it does use virtualization for the ram, that much is true, but the rest is bare hardware
the funny thing is you say this but yet said "no, read it again, the vita emulates the PSP partially (their CPU architecture is similar)," when the vita contains the psp mips processor inside it
Brunocar, with virtualization its not emulation its a Translation of Functions, calls and instructions, far less overhead and its what gives a much better performance compared to emulation. (even on host platforms w/ the same CPU [ this is why DS Emulation failed so hard and DS from SD efforts were shifted to twlloader +nds-bootstrap] in a PSP there *Is* some emulation going on not a 100% virtualization going on (i could be wrong i dont recall if theres something doing the same effect to the PS1 GPU much like the PSP doing w/ the CPU)
a full example of partial vs full emulation is Look at the backwards compatible PS3's the 20 and 60GB SKU's visualized the GPU and CPU (they retained the RSX[GPU] and the EE[CPU] and games run exactly like we see DS games and GBA games on the 3DS. the 40GB model only does "FULL" software emulation (CFW is needed and was only found in safemode and compatibility drops to below 20%) However PS1 playback that is speculation as its been years since i touched a PS3 (kinda got mixed up with a few thngs about Helping a few devs related in bringing OtherOS to FW 3.41+ and my PS3 is we'll just say "Lost.") is Full Emulation in Software, this is atleast true in All Slims and the 40GB Phattie. i'm not certain however if PS1 playback is still emulation rather than virtualization on the 2060 and 80GB models (80's are partial virtualization. as the Emotion Engine(CPU) was removed and Compatibility droped a bit but not to the levels of full emulation)
for the mistaking of "Same chip" there even different Arm7 and ARM 9's for example (newer revision of instructions, better efficiency.) and the host platform plays a key factor. cant just drum up some nifty program to magically make say a PS1 game run on any device sharing the same MIPS processor, alot more time hasto be invested in visualizing everything (and theres still going to be *some* overhead) and making sure it atleast functions before improving for higher compatibilityi'm sure theres more out there that can explain it better than i can and even why the vita cant use certain psp plugins like popsloader