Another advantage of using Ahrefs is their “Fresh Index” “Live Index” switch that displays backlinks that Ahrefs’ crawler found. The main difference between the two is that the Live Index is updated every 15-30 minutes to show live links in your site. For Fresh Index, it is updated at a much longer timeframe, but it still displays dead links which give you the chance to reclaim or change the dead link.
Detailed breakdown of all our key SEO metrics and performance history. It's very easy to compare our performance against competitors, and identify new opportunities to improve. The "link intersect" tool is amazing! You can easily see who's linking to your competitors and not your site, and work through the report list to build your presence on those domains.
One thing I like about Ahrefs is that it's straight and to the point. It's very easy to get in, get your data, and get out. Each report does pretty much what you expect it to. This report shows the referring domains + number links coming from that domain. You can access the links from each domain by clicking the Expand button next to the referring domain:

One thing I don't like is that Ahrefs sometimes does not provide exact keyword search volume. Instead – it provides approximate numbers which confuses us in cases when we think a keyword should get more traffic that it actually does once the SEO content is published. To get the most up to date and exact numbers, you'd better off use Google's keyword planner.
The thing that I liked the best about Ahrefs is that it contains a huge database of backlinks when I've checked my own website and my competitor's websites. This has allowed me to dig deeper and find out their exact linkbuilding and SEO strategies. Ahref contains a lot of tools and features that will make the life of an SEO professional or webmaster who wants more search engine traffic a lot easier. One of these features is the batch analysis feature. Basically, instead of entering your competitor's backlinks one at a time you could actually enter it once. This allows you to quickly check on the SEO metrics for a lot of competitor URLs in just one click.