I've been to Hayman and enjoyed it very much. It compares favorably to any Hawaiian-type resort, even FS. I've never been to an Aman, but my impression is that Hayman is not comparable. It's not the kind of place you will feel like you're being treated like royalty.
Hayman has many of the plusses of a larger resort, including restaurants, shops, and other facilities, without feeling at all built-up. You never feel like you are in a crowd (except perhaps when you can't get a dinner reservation). There is a lot of space. Service is excellent and professional but not all that warm. Every day there is a long list of activities to choose from, including sailing, snorkeling, scuba, etc. The island setting is excellent. Pool is spectacular (obviously). Don't miss the seaplane to the reef.
Given my level of expectation (quite high but not stratospheric), I was very impressed with Hayman Island.