
Price
It would be hard to compare them without knowing current prices. Prices range heavily by region when local resellers may be selling you PS Vita for 220€ and PSP for 100€. It may seam like local resellers of used consoles may know what they are doing for such hefty prices but in my experience this inflated prices are just air. Even their promises of the best condition may be false and direct lie. I personally experienced that.
So if your local resellers ask for such money it would be better to checkout Ebay. On Ebay Vita usually costs around 160€ and PSP around 70-80€. It’s common that Vita is twice more expensive than PSP.
But if you’re not in a hurry in front of holidays you can try Ebay auctions where I personally was able to get Vita for 100€ and PSP for 50€ in relatively good condition from Japan.
Some people on Reddit report ability to buy PSP in good condition for just 35€ but that’s rare. If you’re looking for such prices try garage sales and flee markets, you might be lucky.

Condition
These consoles are both old, but PS Vita is noticeably younger.

If you get PS Vita 2000 then just by the age and good original screen it has the highest chances to be in a very good condition.
PSP is older and has it’s own issues. It uses very unreliable single low profile analogue stick so you most likely will need to open it up and replace the stick. It’s very common that for 50€ you get the drifting one. Luckily, servicing PSP is easy and you don’t need special skills or experience.
Other thing is screen. Screen of PSP is much worse than Vita’s but if you buy three PSPs on ebay of the same model you have a chance to get three different screens. Because they are often get replaced and sadly not all the time for a better option.
Two of my PSPs from ebay have different screens – one of them looks good and other is just garbage by modern standards.
So if you get PSP with a screen that doesn’t look good you most likely would prefer to invest 20-30€ into a better screen. And 10€ into a battery but some PSPs are already sold with new batteries.

Hardware
PS Vita uses much more modern hardware than PSP. It has quad core ARM CPU and GPU supports shaders. It has dual analogue stick. It means that many games of the era were relatively easy to port to PS Vita. There are a lot of multi platforms plus exclusives like Uncharted: Golden Abyss that heavily utilizes PS Vita’s hardware capabilities: touch screen and back touch panel.
Yes, Vita has not only the touch screen but the back of the console is also a touch panel. In Silent Hill: book of memories for example it is used to direct spells. Like a touch pad on a laptop.
For games Vita is using flash cards.
PSP is much more spartan in this case. It’s just a beautiful brick with buttons, one analogue stick, TFT screen and UMD disk reader.
UMD disks are proprietary Sony’s format of small disks. PSP is the only mass produced portable console in the history that uses disks in the portable gaming device.
CPU in PSP is 333 MHZ Mips CPU. GPU uses fixed function pipeline so no fancy effects. It’s still on par with older OpenGL and supports, for example, per vertex lightning and some old school effects so it’s quite good for its era.
Vita has 5 inch OLED on 1000 models or IPS on 2000 models screens when all PSPs are using 4.3 inch TFT panel except PSP Go. Screen of PSP Go is smaller and just 3.8 inch.
Screen resolutions are differ as well. The resolution of PSP panels is 480×272 when PSV is using 960×544. Because of pixel density PSV’s screen looks sharper.
Other difference is in WiFi. PSP has WiFi but it’s so old you will have hard times connecting it to anything. PS Vita on the other hand is using more modern standards and I had no problems with connecting it to my router. Once you have CFW installed you can get games through the internet.

Firmware
It’s easy to install CFW (Custom FirmWare) onto both consoles and run games from a micro SD card. Both are using proprietary card formats so you will need a converter that costs around 3€. You insert a usual micro SD card into a converter and get memory stick or PS Vita card as the result. And yes, PSP and PS Vita use different cards.
For PS Vita you would really prefer to use a really fast micro SD Card like of v30 standard. It reduces the loading time in games. On PSP it’s less noticeable.
I already mentioned that PS Vita is able to download games through the internet. For PSP you will need mini USB cable to connect it to PC and manually copy games. Even installing CFW on Vita doesn’t require you to use PC and done through a specific website.
Games
Both platforms has a huge selection of games. But PSP leans more into exclusives, PSV into multi platform.
Also PSV is able to emulate PSP very well. So if you get PSV you can play most of the PSP games as well.
Your choice
If you think about one of this consoles you probably have something on your mind already. The fact that PSV is superior to PSP doesn’t mean that it’s a clear winner. PSP has a different feel to it. Besides it’s smaller. PSP is the smallest popular game console with 3d capabilities of 3d era.
It’s common for PSP to be re-shelled so you can heavily customize it. People on Reddit even replace mini USB with USB Type-C. PSP is easier to fix and it’s cheaper. Homebrew community is also alive – PSP still gets new games.
I have both PSP and PSV and if you ask me which one I would prefer it will be a hard time answering this. Both. But If select only one for daily use I would still prefer PSV 2000 because of good analogue sticks, nice original screen and easier access to games.
Or you may consider emulation. We have an article about that.