We used enclosed trailers on all of our crews for about 15 years. Just switched over to enclosed a little over two years ago and I'd never go back.
There were two main reasons. First, they are WAY more secure. On the jobsite and at your shop. Now if you're a Solo Op and only have one trailer and are keeping it near your home, it's probably secure. But if you have several crews, I can almost guarantee you stuff will get stolen out of them eventually - I don't care how secure you think your shop is. When it happens the first time you'll be pissed but think it's a fluke. When it happens a year later you'll be like, "WTF! I thought we took measures to prevent this?!" When it happens a third time, despite all your efforts to secure them, then you'll want an enclosed one.
Since we've gone to enclosed about two and a half years ago (and because we hold the crew leader strictly accountable to keep it locked) we haven't had one item stolen during that time.
Second reason is the advertising my enclosed trailers
offer me. It's like a huge billboard rolling around town and sitting in high end neighborhoods all day. And now we have 5 of them going around town any given day. IMO, if you're trying to grow a large business, name recognition is critical. So since that's our goal, the trailers help us meet that goal in a big way. Our name recognition has gone up like crazy since we got these trailers.
I would never go back to open.