- Which is easier to use for emulation?
In terms of ease, it's definitely PSP. Once you have a PSP on cfw, you just have to add files and homebrew to the memory card, no installation and such. For Vita, at the moment, you have to ftp / qcma files and programs, then use Vitashell to install emulators, and then move files around with Vitashell. You can transfer to PSP over USB like any storage devide.
- Which has more systems'
At the moment, PS Vita has everything the PSP has (in the PSP emu) and native stuff too, so Vita has more systems. At the very least, Vita will perform as much as a PSP does. There are still small issues with running PSP built emulators on Vita (directory problems, low compatibility) but they usually have some workarounds. Once the pspemu exploit is released, things should get better on the Vita. Also native Vita emus are getting better daily.
- Are prices for memory cards for the Vita becoming more reasonable, or are they still higher per GB than for PSP?
PSP wins again in this category. Unless you own a PSP go, you can use a microSD to pro duo adapter (very cheap) and use regular microSD cards as storage. Many have reported upto 128gb working on the PSP. There's an adapter which has slots for 2 microSD cards that adds the space. Even the PSP go can be hard modded to use microSD storage. Vita cards are still too pricey and have horrible fail rates, and doesn't look like there's an alternate solution at the moment (people are working on it but it's still in very early research phase, no POC yet)
My advice is, since you're into emulation, buy a used PSP because they're dirt cheap these days and storage isn't an issue, and I believe everybody must own a PSP because it can do so much. The PSP has native ps1 emulation as well, which is near perfect.
Since the PSP is so cheap, it won't hurt your wallet and you can save up and buy a Vita too in future.