ps2 needs more performance than psp.
for good performance in ps2 you need a modern CPU (not older than 7-8 years) with a Passmark CPU Mark score of at least 4.000 (multi-thread) and at least 1.500 (better 2.000 or more) score in single-thread rating.
I guess (i do not know exactly but that is, what i experienced for myself by testing it with several different hardware), that Single-Thread Performance in Emulation is a bit more important than Multi-Thread Performance.
And also important (equal or even more important than CPU power) is the GPU!
You need at least Intel HD Graphics 4000, so a GPU with a 3DMark score of at least 500). And for more demanding games like God of War for example you need a GPU with a 3DMark score of at least 2.000
Here is a list that i did a few weeks ago, when i tested Batocera 5.21 on all PC-systems i have /had lying around at home:
1x means the game was running full speed in native resolution
2x = 2 times native resolution
3x = 3 times native resolution and so on
0x means the game did not run at all or not in full speed
be aware that the ps2 game i tested (bloody roar 4) seems not to be a very hardware power demanding game.
good of war for example does definitely need more performant hardware.