Well, overally pcsx2 is working the same on all platforms and no big deal on comparison. But! For Windows you have a wider choice of plugins, and, as the No1 -- you could use GSDX. For Linux and Mac's you stay with ZZogl (or ancient ZeroGS OpenGL). So windows users have a perk.
To get an answer to question, will it run, you should name videocard and CPU.
3870 will be o'k on proprietary drivers. You could use even AA 16x on many games.
I mean do I need to install nvidia driver for pcsx2 ? while using ati card ? will it work ?
No, you need to install ATI proprietary driver.