Am i gonna notice any performance drop by switching from the PS2 being my main console to the PS3?

I really wanna get a PS3 because of its great game library. But as i look for PS3 games performance on youtube, alot of the 3rd party games have an ustable frame rate, and i worry that this might make my PS3 experience very bad to the point that i don't wanna play with it anymore. I know that the PS2 doesn't have great performance nor HD resolution output either, but it has much more stable frame rate than the PS3, so this makes me feel like getting a PS4 and solve this dilemma, but i still don't wanna miss on the PS3 games, any thoughts?