What do you like best?
The best feature of Majestic is the Trust Factor (TF) and Citation Factor (CF) numbers - as of right now, they are the MOST accurate SEO numbers in the industry. Back in the day, it used to be Moz's DA PA, but they have stopped updating it and most of the time it gives of erroneous numbers that mislead.
I also LOVE their Chrome plugin which allows me to quickly see the TF CF of any site I am currently on. Bravo!
What do you dislike?
I have only 2 issues with Majestic, one small and one larger:
1. (small) It's not exactly a pretty or well-designed site. Pretty archaic in its appearance - unlike its competition.
2. (large) While Majestic's blog is pretty excellent, they fail to provide adequate, easily found PDFs or training to help new people understand what TF and CF is, and other functions that are useful.
Recommendations to others considering the product
Make sure you understand what TF and CF really are. It's not so much about how high they are...but where they are together. I'd not suggest a cit that has a TF of 21 but a CF of 2 or vice versa. I'd rather see them about the same. So a 16 and 16 would make me happy.
What business problems are you solving with the product? What benefits have you realized?
This helps me choose which places to guest post, which bloggers to network with and ultimately, where relationships should be built. Furthermore, it helps me to track my own site, where Majestic thinks I am in terms of trust and citation ratios, and helps me see what backlinks are pointing to my website. Another important feature for me is the anchor text ratio. That little pie graph helps to make sure I am not over optimized and helps protect me from potential penalties.