Universal fight stick or specific system stick?


i’m buying a lot more older ps2 fighting games i never had and i wanna get a stick but i’m not sure what i should spend money on. i really wanna get a stick for my xbox because i have sf4 for it but i also wanna get some other fighting games for xbox. but i all the fighting games i have for ps2 i think i’m going to end up getting a stick for that. my question: are there any universal fighting sticks you guys recommend that work for xbox360 and ps2 (probably ps3 since it uses the same controller port)? also, if i end up getting one specific for ps2, which will work cuz i have a psx-usb plug, what sticks do you recommend that are good, and relatively inexpensive, for ps2?