Majestic could be classed as a one trick pony, it's great for checking competition, backlinks etc. The Inbound feature in Referring Domains Site Explorer Report, is a nice feature.
It's cheaper than Ahrefs, but it depends on which metric you choose to determine rankings and domains.
The new Related Sites feature is another nice addition.
If you go with TF/CF, then this is the one for you. Topical Trust Flow, some people like, but it's not the be all and end all.
@splishsplash did a nice write up on how these can easily be manipulated.
AHREFs is like a Swiss army knife, it's ideal for checking competitors. It's also got a great keyword research tool in there.
The DR as a metric is quite accurate, in my opinion more so than DA from MOZ.
I can put a domain into AHREFs and scroll down the page and immediately see anchors, so if I'm considering buying and see it's full of porn/Chinese/Japanese text, that alone stops be going any further.
AHREFS is also great for ranktracking and reverse engineering sites. The Content Explorer is another really useful tool, if you use it.
Dixon Jones and Tim Soulo are both nice guys, share some great information on how to get the most out of each tool.
If I was going to pick just one of these 2, it'd be AHREFs everytime.
