As mentioned by jurgenwerk they both have their own version of "DA" pretty much only Google knows your "DA" they are just making an educated guess based on backlinks and other factors.
I found two sites that offer the same info for free. websiteseochecker.com's "Domain Authority Checker - DA checker - Check domain authority" and smallseotools.com's "DOMAIN AUTHORITY CHECKER."
Stick to the provider you trust more and perform domain/page authority comparisons in the scope of a single SEO metrics provider.
Personally, I think Ahrefs is more accurate. Their crawling bot is supposedly the second most active bot after Google.