Pentium is the lowest range in the Intel lineup, designed purely for budget systems. Core i3 is better.
One way to think about it (and grossly overgeneralizing it)... Pentium range has 2 cores, Core i3 has 2+2 cores (thanks to hyper threading), Core i5 has 4 cores, Core i7 has 4+4 cores.
The +2/+4 cores are logical cores, not physical cores, which run between 50-80% of the strength of a physical core. Having more cores means more threads can be executed at once (good for multi-threaded applications, not so useful for single-threaded applications). Most emulators are only single-threaded, which is why they used to say to emulate PS2 you needed 3Ghz minimum and the faster the CPU, the higher framerates you got. I stopped using emulators altogether around that era so I've only heard that Dolphin is multi-threaded and multi-threading hacks exist for PS2 emulators but I don't know the details.