We have done the comparison posts around these tools here https://bloggerspassion.com/semrush-vs-ahrefs-review/ and here https://bloggerspassion.com/moz-vs-semrush/. Please go through both the review posts and go with the SEO tool which fulfil your needs. You can also try Free trial for these SEO tools. And go for the premium version of a SEO tool which you feel is best for you.
The Backlink Analytics tool can provide lengthy lists of competitor's backlinks that can be exported in spreadsheet formats. You can see your competitors backlink strategies including legitimate (blogs, directories) and illegitimate methods for gaining domain and site authority on Google. I also appreciate the keyword rankings, as it allows for easy reporting and tracking of SEO optimization strategies and keyword campaigns. Great tools for tracking keywords campaigns against similar business as well.
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.
SEMrush Keyword Research feature gives you tried and tested keywords that can help you in improving your website rank in Google’s and Bing’s top results. It also provides you with the value of these keywords in paid as well as organic search, and which top players are using them in their landing pages. There are ton of useful data outside Google Adwords.
Ahrefs boasts the best link database among any system out there. It does most everything -- link monitoring, alerts, calculated metrics, the richest clickstream blend out there, and much more. Its UI is cluttered in a good way and the company has quick and polite support. And Tim Soulo -- the public face of Ahrefs -- has done a ton of good for the SEO community.