When I first started SEO there were 3 big guns in three search marketing world.
- Majestic for Backlinks.
- Mox for SEO
- SEMRush for SEM
I still think those 3 are they best in their realm, and with an unlimited budget, I would pay for all 3. But I don't have an unlimited budget, and I to had to pick just one, so I set out to do some research like you did. Upon further review, I did found that someone actually basically did the baclkink study for me!
http://www.analyticsseo.com/blog/link-data-research-majestic-seo-moz-linkscape-ahrefs-part-2/
They all have their pro's and con's, but for me, Moz seemed to be the best bet. I looked at is as an investment. I felt that in the long run, the quality of links that Moz were finding was more important than the extra links that Ahrefs or Majestic were finding. My second thought was that as all these companies grow, Moz, seemed adapting to the needs of modern SEO better than the other companies. So after weighing the pro's and con's I figured it was worth it and would only be a matter of time before Moz's backlink tool was more powerful, or would outshine the others simply because of efficacy.
So far, I am pleased.
As I said, with an unlimited budget, I would have all 3 programs. Moz, SEMRush, & Majestic. I can't, so I choose Moz, any day.
Hope that helps.