There's definately pros and cons to each. No one can say one is really superior to the other. I've only used open trailers in my 15+ years though I still want an enclosed just for the cover for the machines not in use, place to pee, and "security" though that's not a huge issue where I'm at either. The cons I see are accessing things, grabbing a trimmer or edger can be harder since you have to open a door and possibly squeeze past a mower or climb over one to get to them. Fueling would be more difficult obviously, but ordering a trailer with a drivers side door or a fuel door is an option. They are considerably more expensive, double the price at least and tripple to get one with the added doors and better framing, vents, etc. Height is an issue for me, being 6'4" tall, though you can order them taller than standard as well. Weight is also a factor, they are heavier than an open trailer, and you may have to step up to a heavier axle, which then could put you over on your weight maximum into CDL range.
Open trailers it's easy to access anything from about anywhere around the perimeter of the trailer. Trimmer/blower racks face outward and are accessed from the outside of the trailer. Cheaper. Easily modified or repaired generally if you can weld and fabricate. Tool boxes can be added for storage and gas cans and mower fuel tanks can be easily accessed. Can be backed into most garage doors (height wise). Lighter and easier on the truck. Cons are having everything out on the open, easier for someone to steal something unless you use a lot of locks and cables to secure things. When it rains everything you own gets drenched. The sun also is beating on everything all day every day weather it's getting used or not. Better find a bush to pee behind...
Hence why I've yet to make the jump to an enclosed. It's about a $10,000 investment and I really fear having buyers remourse because of the cons I listed. There's quite a few guys locally that use them though and I think they get along with them ok.
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