The highest tropical marine diversity in the world is off Northern Sulawesi in Indonesia. The Carribean is nearly the lowest.
The Red Sea, Indian Ocean and its nearby seas Including IndoPac are unquestionably the best for both quantity and quality of marine life and (possible) visibility. The south and western Pacific Islands are close behind.
There are well understood and well documented geological reasons for this. I have been fortunate to dive all of these areas and more (non-tropical). My personal experiences support these observations very well.
Australia's Great Barrier Reef would be in that latter category as long as you stay away from the most popular dive sites that suffer from too much diving pressure. Many of those areas have become somewhat mediocre.
Western Indian Ocean drops off to mediocrity and the Atlantic is just not in the same league. The Med is Dead is not just a cute phrase. It is a tragic truth. There can be excellent visibility in saphire clear water virtually devoid of interesting critters.
I personally like the Red Sea a lot for a quick, short trip. A couple of weeks on a small (6-10 divers) liveaboard in the Maldives is a great trip offering beautiful and varied scenery, dive types, benthic and pelagic fish, corals and other critters, but their smaller liveaboard generally only average 2 dives per day plus a couple of night dives per week. These may not be the very best dive locations but I like them.
The area around Papua New Guinea/Borneo is high. quality. My all time favorite is a sequence of 3 or 4 IndoPac trips on small liveaboards, 1 week each, separated by a few to several days ashore to help preclude, or even cure, ear infections and get in some extended decompression and some local culture between intensive diving schedules. I do not like large liveaboards, at all. On a long trip like this it is wise to extend the time before flying by an extra day or two, particularly the farther away you are from being a 19 year old. Our dive charts were originally based on very healthy young males. Some of us no longer fit that fitness model.
The main thing is to dive safe and dive fun with safe divers. Good diving to all, where ever you choose to get your nitrogen fix. All diving does not have to be at the best ever locations. Some of my most outstanding dives have been in low vis with not a huge amount of critters around. But maybe I saw something for the first time that I had wanted to see. Or I got to move amongst huge shoals of Moorish Idols (Red Sea in May/June)or witness some really interesting behaviors like a harem of giant Stellar Sea Lions swarming all around us in Alaska at night, admittedly in low vis, frigid water...and dangerous...adrenaline rushes...exciting!