So why my pc can run more powerfull systems so well, but the psx emulation go so bad?
Because it is not about how powerful the original system is, it is about how the emulator was designed (see http://emulation.gametechwiki.com/index.php/High/Low_level_emulation), beetle-psx is more on the LLE side, i would recommend pcsx-rearmed instead if your computer is not fast enough.
Emulators generally don't care about the cpu generation, the number of cores, ..., they only care about cpu frequency : if your cpu is at 2.4Ghz, for beetle-psx your computer is as good as a 2.4Ghz single core pentium from 15 years ago, which is kinda crappy to run this emulator.
A small other question, is there any way to avoid the green screen when starting a neogeo rom?
No, this is present in original hardware. I know there is a trick to hide it, perhaps i'll look into it the day there won't be things more important to do in the emulator, which means probably never. I don't mind if someone try to add a core option for this and make a PR though.