I have used all three although I haven't used propane much. For me, it comes down to how you use the boat. If you are sailing around the world, it would be diesel for me. If you went out on weekends, it would be wood. I can't see any scenario that I would prefer a propane heater over one of the other options.
It should be noted that most "wood" stoves actually burn wood pellets or charcoal. There are some stoves that are made to burn good old wood. The problem with collecting driftwood is that the shape is really weird and it is very hard to store. Storing nicely chopped wood or pellets isn't too bad if you are going out for a few days at a time. It should be noted that wood takes a lot more human input. It is harder to light (your fuel can get wet), you need to stoke it, and you need to dump the ashes. If you want something that you can leave on overnight, diesel is probably better.
I have a lot of experience with the Refleks heaters which are essentially diesel pan heaters. They will stink a tiny bit when lighting and shutting down but once you get good at it, it is hardly noticeable. I have actually never had to fix anything on one of these stoves. The schooner that I used to work on had one that also ran 3 radiators throughout the boat and that was really nice.
I don't really like propane because it is harder to refuel, you can't get the fuel anywhere, you need more safety devices and I like to have as many things be diesel as possible(one fuel is great).