Was just at AKR last week, and would recommend it without hesitation. I also have heard good things about the other two and think you would be fine at any of the three. AKR is on the north side, and CCV and FI are on the south side. In general (there are always some exceptions) the winds blow from south to north off of the mountains in Honduras, making diving conditions on the south side generally a little rougher. However, the underwater topography on the south side lends itself to steeper walls and depending on who you talk to, the diving on the south side may be slightly better than the north side, although I was perfectly happy with what we saw on the north side from AKR. During the week we were there conditions were very rough on the south side of the island, to the point that for the last two days of the week, there were several people from FI diving with the operation at AKR because it was too rough at FI, and the scubadiving.com board had a story of a guy giant striding into a swell and getting thrashed against the back of the boat pretty hard. So if you are the type who gets seasick easily or doesn't do well in rough conditions, the north side may suit you better.
In regards to the time of year, I may be slightly off on the start, but as I understand it from one of the instructors at AKR, October through January is the rainy season, and it pretty much can rain non-stop at times, which seriously affects the vis underwater. If I were planning a trip in the fall, I would go earlier rather than later to give yourself as good a chance as possible of dodging the rain. Also be aware that Sept-Oct is the peak of Caribbean hurricane season, and although they are low in latitude, they have gotten some significant storms recently (Mitch in 97-8? was in october, and Lily hit southern Belize in October 2001). So trip insurance that covers weather would not be a bad idea that time of year anywhere in the Caribbean.
Hope that helps...
AggieDiver