You may want to do a parity audit on your mobile or desktop but it might not be necessary. This will help you figure it out. If you do it when you don't need to it won't hurt anything but will waste your time which is valuable. It's more efficient to wait till such an audit is needed before taking time out to perform it. You can use that time to do more important things.
Is the mobile version of the website “optimized” and crawlable?
A mobile parity audit will also improve rankings by identifying errors or duplicates on a mobile site.
There are four simple steps to begin a mobile parity audit: crawl the site as a user, then as a mobile user, combine outputs, look for errors and differences.
“You should do a parity audit if content is added, removed, hidden, or changed between devices without sending the user to a new URL.”
Read more: https://moz.com/blog/mobile-parity-audits