I've been to both Cobalt and AKR and they are really different places (but loved them both). On GC, we've always rented a car because it's the best way to get around since there really is a lot to do/see all around the island. Lots more shopping, restaurants, etc... If I recall you can arrange with Cobalt to pick you up at the airport and drop you back off there. They do have good shore diving right off the hotel but if you want beach, shopping or sightseeing then it's better to rent a car there.
Granted we were on a group trip when we went to AKR but we only left AKR once to do the zip line because there's so much to do at the property and not as much to do around the island as there is on Grand Cayman. You'll be so busy with things to do at AKR, if you want to go into town once I don't think it costs much to get there. The landscapes of both places are so different, GC is pretty flat with few bugs and not as much vegetation as Roatan. Roatan is hilly and loaded with trees and vegetation (and BUGS), more of a true paradise feel to it. I haven't been back to GC since 2005 but the diving was more pristine, better visibility and awesome walls. Roatan is nice because it has some great pillar coral, fun wrecks and other interesting dive sites.