What does the company do well? Ahrefs is hands down the best 3rd party backlink tool. It appears to have the best database of backlink data, has a great interface for navigating that data, and has a plethora of additional features added-in as well that are invaluable.
What does the company not do well? Ahrefs is a little expensive. Depending on the plan you have with them, you may find yourself being asked to upgrade to a more expensive plan as you navigate through the interface.
What about the company do you wish you had known before purchasing? I was fairly familiar with what I was getting prior to purchasing, but to new users, I recommend looking at the pricing structure, especially if you're interested in hooking in via API.