In my experience, mesh likes to get caught and it rips easily. I learned the hard way at a crappy amusement park years ago that Mesh and I don't mix well. When you're getting on and off rides quickly, your bag could potentially snag on things. One little catch and my mesh bag has a huge hole in it. I avoid Nylon for much the same reason. I work in a school and I see those Nylon drawstring bags unraveling after the kid pokes a pen through it by accident.
I use one of the Disney cinch ones with thicker straps (They're around $23 or less) and it isn't terribly hot or gross-feeling on my back. (IMHO, there is nothing that keeps me cool in a Florida Summer except for Florida AC!) It isn't like a traditional backpack in feel I don't think the drawstrings are terribly annoying at all. I can basically whip it on and whip it off pretty easily, which comes in handy. I have had the same one for about 7 years. I had a friend go and buy me a replacement and I have it brand new and ready to go. I haven't had to use it yet.
If you have the mesh bag already, give it a try. Best case scenario, it works and you love it. Worst case scenario, you hate it and you'll buy a bag in the parks or try again next trip.