Is that pronounced “peace” or “piss”?

More like pi+[y]es, but single syllable and no y.

EDIT: Here are three audio files to hear: https://pl.wiktionary.org/wiki/pies#pies_(j%C4%99zyk_polski)

When do you use that vs собака (sobaka)?

I don't, I'm Polish. Can't say for sure for Ukrainians, don't know Ukrainian that well, but my reading of https://en.wiktionary.org/wiki/%D1%81%D0%BE%D0%B1%D0%B0%D0%B... and https://en.wiktionary.org/wiki/%D0%BF%D0%B5%D1%81#Ukrainian suggests that пес must be male, but собака is either male or female. I might be wrong.