One of my favorite things is the SEO Ideas module where it gives you specific things you can do on each page that will help you improve your organic traffic. While you can figure some of this out through the normal audit, having these extra ideas helps with getting the creative juices flowing. There is also a very large amount of competitive research, content idea generator and so much more. It's astounding what all is there!
Ahrefs isn't cheaper and has a less appealing interface and layout. SEMrush is aesthetically pleasing, but you need to be willing to allocate budget to it and to make use of the comprehensive array of tools it brings to the table to recoup that investment. Free plans might suit if you only want 10 keywords to look at; if not, buckle up. Use it right, and it'll be worth it.
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.
We use the tool mainly to help with our SEO clients. Personally, I like the rating tool on the page. I think it's a great way to compare your page with the top 10 ranking pages for a specific keyword. The site audit in particular can offer quick answers. SEMrush is our main SEO tool and really does it all, especially with the massive updates from last year. Track keyword ranking positions, offer some keyword search tools and compare the domain with others related to it. You can also automate reports that are labeled blank. It also performs domain analysis, tracking of backlinks and audits of sites that we use all the time in our SEO business.
Pros: SEMRush is a full-fledged powerhouse for SEO building strategy and SEO audits. It's pretty beefy, so I would only recommend it if you have the time and patience for SEO, as the software gives a ton of outlets in looking up actionable items for your SEO Strategy. The first thing that I really liked with SEMRush was the initial SEO audit of my site -- I was able to see what's good and what's bad about my SEO, and the quick errors or warnings for title headers and ideas for gaining more traffic was awesome. Moving on, I found their analytics just as good as Google Analytics, showing me where my traffic is coming from and where I can improve my paid search positions. I haven't used the Social or Content aspects of SEMRush but social listening looks to be baked in well and integrated nicely. If you're in the market for seeing how your organic and paid search traffic plays a part, and then strategizing in how to improve your overall position against organic search and then your competitors, I'd recommend SEMRush.