Cloth is the way to go for me:

-You can fold it up and stuff it in your luggage if you travel.
-Cloth absorbs sweat which can keep you cooler AND keep the sweat out of your eyes (However, I found the Tilley not to be very good at the sweat out of the eyes thing).
-Cloth can be put into the washer after every hike, camp out, or what not if it gets grunged out.
-Cloth can be dunked in a stream to keep you cooler (or you can stick snow wrapped in a bandanna if you're up high and there are still snow banks).

HJ