Hooked....it would depend on what you want/need other than diving. CCV and AKR both have excellent dive operations. AKR is on the north side of Roatan, CCV is on the south. As such, their dive sites differ a bit and the conditions can be vastly different on the same day. For instance when we were there in October with the storms in the area, the north side was having 6-8 ft seas while the south side was flat. The time of year you go and the weather at that time will help you decide which side to stay on.
Also if you require non-diving activities and don't want to leave the resort for them, if you need some night life then AKR would be a better choice for you. Keep in mind that although they have the museum, the dolphin research center, a great gift shop, most of their rooms/cabins are on a key and you'll have to get someone to give you a ride back and forth in a boat. Not a big problem as they are always ready to do so, but it does take more planning than just walking to the clubhouse. There are also several steep hills and the clubhouse has a long stairway you have to climb for meals. This is the main reason we decided not to stay there...my knees just wouldn't take it! It's also a family resort so there can be lots of children around.
If diving is the main reason for your trip then CCV would be the best choice. CCV is on an island by itself so if you want/need to leave the resort you'll catch a boat to the main dock. This has never been a problem for us. There are several non-diving activities planned every week that you can sign up for, such as shark dives, treetop canopy tours, shopping trips and eco-excursions. With boardwalks everywhere, it's easy to get around the resort. It's an adult resort so there won't be any children there although Jr. divers are welcome with their families. CCV may not be the cheapest of the 3 you mentioned but IMHO it's worth the extra $$.
I've visited FI several times with the thought of taking advantage of their cheap rates while still diving the same sites I love. But I gotta tell you each visit made me even more convinced not to stay there. There was always a sewer smell, the rooms we looked at needed lots of work and the guests we met weren't very friendly. Might have been a cultural thing since we saw very few Americans there. K8 mentioned the loud music. If it can keep me awake 100's of yards away, I can just imagine how loud it is right there with it. Most days it starts at dark and is still going after midnight.
Just my 2¢