This report can help you reverse engineer, down to the day, a link building campaign that your competitor is running (always good to be out in front of a big link push by a competitor) and can also help you evaluate your own link campaign or even help you spot a link growth issue that may have resulted in some kind of penalty or over-optimization filter.
Of the three popular backlink reporting tools (Majestic, Moz, Ahrefs), Ahrefs provides the most useful link data. Even in other areas of SEO, Ahrefs seems to always keep their toolsets fresh. They continually add in useful tools and features that make other software suites less relevant. The most recent addition is their site audit tool which provides a beautiful visualization of technical site issues.
Its interesting that you overlooked Ahrefs site audit tool. Unlike SEMRush which limits you to 20,000 URLs, Ahrefs can crawl very large websites. Their data explorer is by far the best in the business. SEMRush gives you a list of URLs with issues they want to identify. But no option to customize. Ahrefs, much easier to use and powerful Data Explorer are very powerful indeed.
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.