Yes, there's one thing you didn't do while building that system you didn't thought that lots of PS2 games simply require a better hardware;].
APU's are totally great, if you want something to browse the net, make an media center or get it for work, but in terms of ps2 emulation, your cpu is average at best and that radeon does use your system ram which is way slower than gpu's dedicated memory and even if that wouldn't be the case HD6500 series was for very low quality gaming even at their normal versions. Unfortunately for you ps2 games need quite fast memory transfers hence probably that radeon is the first thing to limit you, especially if while building it you also were cheap on your RAM which heavilly affects that integrated radeon>.>.
Check "native" in GSdx config(GS plugin) and generally forget about higher res, you might also try if "allow 8 bit textures" affects your fps there since it could help with those limitations.
Also check what's EE% at the top of the window when you run the game shows, if it's close to 100% then you're also getting cpu limited hence experiment with some speedhacks or at least try different presets in config>emulation settings menu.
But generally while you might work something out of this, don't make your expectations too high, not on a budget system at least(and if you have also ZoE2 just forget about it, boss battles require something like an intel cpu OC around 4.5ghz on pair with decent gpu @
[email protected]).
Each game has different requirements, if nothing helps you would do better trying to play other of your ps2 games than irritating yourself with slowdowns.
