Hi,
I live in Jordan and dive in Aqaba very frequently. The diving in Aqaba is very relaxed and there are some nice sites. Mostly coral gardens, pinnacles, and some wrecks. You wont find the high density and the sheer size of similar species in Aqaba as you might encounter in Egypt - things are a little more "scaled down" , but the diversity is still very good and the general health of the coral and marine life is excellent. I have heard from several friends who have dived both Eilat and Aqaba that the sites in Aqaba are significantly better and healthier... but I cannot comment on this personally and have no experience diving in Eilat.
Of all the Dive centers in Aqaba I would very highly recommend Sinai Divers (the same company that operates out of Egypt). They have a great team, skilled dive guides, and offer both shore and boat dives. They also keep their equipment very well maintained and up to date. They may be a little more expensive than the other dive centers in Aqaba as they are actually located in the Movenpick Resort in Tala Bay - but I have not checked recently. Ask for the General Manager Sacha - he's a great guy and will go out of his way to make sure you get what you need. Have a great trip and enjoy Petra (you won't forget it - it's a phenomenal place) and have a great time in Aqaba.
cheers,
Nasser