You mean the PS2 Classics version of Persona 3? It's an emulation of the original PS2 game. So it should work identically bar emulation flaws.
Don't think it's uprendered either, so the same resolution.
You will, of course, notice a difference if, say, your PS2 used composite cables and your PS3 uses HDMI, the latter is a lossless signal, and much better than composite.
But otherwise, yeah, same deal.