In recent years it might be easy to assume that wet is better than dry because there are more wet systems being introduced. I personally don't think there is a simple answer as to which is best, because it depends on a raft of individual circumstances. But both systems are quite capabale if selected and used correctly.
Caravan manufacturers may have a preference towards wet systems because of their smaller pipes which are easier to design into a caravan, in particular the routing of the water pipes is less critical compared to hot air ducts.
Technically water is a fantastic heat carrier, you can move more heat with water than you can with air. So it's necessary to balance a number of factors when designing a caravan.
Water systems with their better heat carrying capacity will tend to suit larger caravans - which is why the have so far tended to be fitted to top range and larger caravans. But whilst you can move the heat around the caravan more easily you then need to consider how to release that heat which usually involves a radiator (Or more accurately heat exchanger).
Floor space is generally at a premium in caravans so radiators tend to fitted inside seat lockers. This creates further issues with having to provide ventilation slots at at the back of the seat and a false wall to allow the convected heat to rise. Unfortunately this also usually means the radiator is effectively heating the locker as well, and that is not always a good thing and it reduces the heat available to the living space.
The radiators used are designed to maximise the convection of heat. This means the warmed air will rise simple because of its increased buoyancy compared to the cooler air around. This is rather gentle process, and it leads to the warm air collecting at the top of the caravan, and at the same time leaving cooler air closer to the floor. This leads to hot head, cold feet situation.
The same will occur with a basic gas heater, but the introduction of the blown air system puts mechanical energy into throwing out the hot air at floor level. This moves the air more vigorously which causes it to mix in a way that convection cannot match and it will reduce the top to bottom heat gradient effect. Installed and adjusted properly a blown air system can reduce temperature difference to less than 5C! Wet systems will be lucky if the difference is less than 10C!
The lazyness of the convected air from a wet system is the main reason why wet systems seem to take longer to thoroughly warm a caravan. So if you are particularly looking for a fast response go for blown air. Over a longer period there is less to separate the systems.
Blown air requires the fan to be running, and even though they are reasonably quiet, the wet systems will be quieter.
As for power consumption, that difficult to compare, as the power used by the blown air system is variable depending on the duty set by the the thermostat, and the heat losses of the caravan.
There's no danger of leaks with a blown air system, and ducts are easily repaired or replaced. Water pipe repairs are a bit more involved as is the need to ensure it is fully leak proof.
So it's six of one and half a dozen of the other. I hope this may help you decide.