The backlink index is one of the best too though at the time of writing, Moz has just improved their index. Regardless of index size, which theirs is large enough, the type of data they provide is the most useful. The broken links data is probably the most useful that isn't easily matched by other tools. Additionally, going back to the content explorer, you can find unlinked mentions, a feature that appears to have been removed in Moz's "new" tool (I may just not be able to find it).
I can recommend Ahrefs to anyone in search engine optimization, social media marketing or digital marketing. Ahrefs is perfect for keyword research, competitor research, viral content research, web page audit, rank tracking, competitor tracking and more. If you are looking to find great link opportunity then Ahrefs is the tool winning in that domain.
Ahrefs make use of two link updates in your website - the Fresh Index and the Live Index. Fresh Index which updates at a longer time frame. It shows the dead links on your website, giving you the chance to change or reclaim the dead link. The Live Index, on the other hand, makes link updates every 15-30 minutes. This provides you with the chance to see regular link updates on your website.