What does the company do well? Extremely likely, between the simple setup, automated migrations and great support when you need just a little more control, WP Engine has not failed me yet.
What does the company not do well? There seems to be times when the admin side of a site seems a bit sluggish. This is usually during peak hours, but if your site is on a server with other sites that have heavy loads, you can become affected. But you can usually ask them to move your site to another server and they'll take care of getting you to a more reliable environment.
What about the company do you wish you had known before purchasing? I wish, and still wish, that I knew what kind of resources are allotted to each installation. No one on support seems to be able to answer this question.