Should I trade my ipod mini for the big one?

I have a silver iPod mini, pretty much brand new only a few hunded songs on it. My brothers gf has the full size one with like 1500 songs on it. Plus a pink iSkin. She wants to trade me for mine... I probly will do it. But im wondering if it will be compatible to use on my comp. Because I do know that each iPod will work on the comp it is installed on with original cd. My sisters didnt work on mine, mine didnt work on her cpu. (That is how I know). Unless there is a way around it... what do you think.