I had a set of Tory (I think) web reins that I adored. They stayed soft, the grips were spaced well, and at 3/4" were substantial enough to keep a hold of. However, they were the only pair of web reins I ever liked. (It helped that they were red and black, and my teenaged-eventing self thought that was AWESOME!).
I do prefer rubber reins, I feel that leather reins are too soft and thin in my hands. Plus, my horse is a copious sweater, and I need all the grip I can get.
ETA: regarding melting rein rubber, I have heard multiple times that fly spray is very tough on rein rubber. I make sure that I avoid spraying the line of his neck where my reins go to prevent it. Even my cheap-o Treadstone reins are in great shape after eventing in 5 years of hot, humid VA summers.