Comfort is an important element of SCUBA, as a dive should be about enjoying the sights and the feeling of the underwater environment. Most divers have experienced some sort of nuisance on a dive, whether it be a leaky mask, a too-thin wet suit, too much or too little weight, or even uncomfortable fins. Just one such annoyance has the potential to significantly detract from the dive.
This is the strongest argument in favor of the full-footed fin. Assuming you've chosen a fin that fits, you slip it on and dive in. There's no worry about booties, annoying buckles, or a chafing strap. It offers a consistent comfort that you can rely upon. Also, full-footed booties tend to be much lighter than their open-heel counterparts, meaning less leg work.
In relatively shallow, warm waters lacking much of a current, full-footed booties will offer a comfort and convenience that can't be matched by open-heeled fins.
Durability is an area in which open-heeled fins gain an advantage. Because the full-footed fin is one large piece, if any part of the shoe deteriorates, the chances are that the fins are useless. However, because the open-heel fin has several components, you can replace worn parts with greater ease. For instance, many brands sell replacement buckles and straps.
Because of the very nature of the construction of the two fins, open-heeled fins tend to be made out of slightly heavier, but more durable materials. Full-footed fins need a comfortable shoe, as the diver does not wear a bootie to protect against chafing, and this forces manufactures to use softer, less durable materials such as rubber.
Functionality is perhaps the most important element of a fin. If a fin feels great but has no propulsion, it's useless. Open-heeled fins are superior in propulsion.
If heavy paddling, such as against a current, is ever necessary, a correctly strapped fin will never detach from the diver's foot. The same cannot be said for a full-foot fin, as they will, by design, detach from the foot if enough force is applied. This is particularly crucial if you are diving at depths below 20 feet. If you are deep and lose the fin, it is possible you will never recover it, as the fin will ascend at a rate too quick for you to safely chase it without risking decompression sickness.
There is a limit on how powerful a full-footed fin can be. Because too much force leads to detachment from the foot, designers are not able to create the same heavy-duty styles that they can for open-heeled fins. Because you are weighted down significantly in deeper, colder water (due to wet suit buoyancy), you likely will not find full-footed fins will give you the kind of power necessary to propel yourself with ease.
When making the decision between a full-footed and open-heeled fin, you should consider what type of diving you intend to do. If you are in shallow, warm water with little current, such as shore diving or some reef diving in the Florida Keys, the convenience of slipping on a light, full-footed fin might appeal to you. But for deeper diving, and any diving that requires thick wet suits, open-heeled fins are the way to go, especially because in colder waters you will want to wear the booties anyway to keep the feet warm.