I've never worn a standard LT Tilley, but I'm really happy with my mesh version (LTM6). I went with the airflo because I work up a fearsome sweat in no time flat, and while the mesh doesn't keep me "cool", it does let in some nice breezes. As far as rain is concerned, I rarely use my jacket's hood anymore unless it's really pouring. The mesh does let in some water, but just enough to keep me cool while walking.
Two things to consider, though:
1) Don't go nuts and cut off the hood of your rain jacket just yet. The Airflo hat is great in most all conditions while moving, but when standing in the rain around camp you're still going to want more serious protection from the elements.
2) I agree with the previous poster that you probably shouldn't buy one without trying it on. I had to try three different hats before I found mine.