JPCSP is a PSP emulator written in Java. It requires Java Runtime environment to be installed. It's more advanced than PPSSPP, but the other should overtake it soon.
It requires the Jave Runtime Environment to be installed, which has a history of security issues. Because it uses Java, it is also much slower than PPSSPP. It is recommended to use PPSSPP instead, and only to use JPCSP if a game does not work. Development of PPSSPP is rapid, and it will soon overtake JPCSP in terms of game compatibility.
Java is better for debugging, which is the whole point of JPCSP. They never meant for it to be a standard emulator. They made it so they could understand the PSP's inner workings better. And thanks to the JPCSP team, PPSSPP is developing at breakneck speeds. Both teams communicate a lot and contribute with each other. Just look at PPSSPP's code for pgf and tell me what you see.