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1. I'd prefer to stay at home rather than go out.

2. I'd prefer staying at home to going out.

Would it be wrong to use than instead of to in 2?
Comments  
I would prefer to stay at home rather than go/going out

I would prefer staying home to going out.

I (would) prefer gerund to/over (never than) gerund.
Diamondrg1. I'd prefer to stay at home rather than go out.

2. I'd prefer staying at home to going out.

Would it be wrong to use than instead of to in 2?

2. I'd prefer staying at home to going out. ('than' cannot be used)

You could also write: I would rather stay at home than go out.