Advantages of an enclosed is security, keeps equipment dry and out of the sun. Disadvantages, cost more, harder to pull in windy conditions, (Chicago, the windy city) can't pull into a gas station and fill up the mowers on a big trailer unless you unload the equipment. You need a big tank in the back of the truck to fill them or lots of cans.
I have both, but I use the open trailer to work out of. I was using the 24' Haulmark enclosed trailer for storage, but now have my stuff in a garage across the street.