Learn English – which one is correct ” to+verb+rather than+(verb+ing or to+verb)

Either is correct, but this form is usually constructed with a parallel structure.

I prefer living with someone rather than living alone

However, when the main clause is written with a to-infinitival verb, we usually use a bare-infinitival verb after rather than.

I prefer to live with someone rather than live alone

It's also possible to use the -ing form, especially when the rather-than structure precedes the sentence.

Rather than living alone, I prefer to live with someone.

Reference

Practical English Usage(PEU) Second Edition by Michael Swan