"I´d rather you stayed than go." You're mixing past and present here. If you are talking to the person NOW, then, "I'd rather you stay than go."
If you are talking about the past, "I'd rather you stayed than left." You can also use "went" in place of "left."
"I´d rather you stayed instead of going ." Again, mixing past and present. Stick with one tense and you'll be fine. :-)