According to this JLPT study site, the two are interchangeable in terms of meaning. As for how common they are, I searched for both terms on BCCWJ. なくても had around 10,000 entries whereas ずとも only had around 500. ずとも is somewhat formal sounding and it may only be used in written Japanese or formal styles of language.

According to this JLPT study site, the two are basically interchangeable in terms of meaning. As for how common they are, I searched for both terms on BCCWJ. なくても had around 10,000 entries whereas ずとも only had around 500. ずとも is somewhat formal sounding and it may only be used in written Japanese or formal styles of language.