I may go with Tilley after all. I like the fact that they specialize in hats. I noticed that most of the gear I end up really using and enjoying using come from manufacturers that specialize in each type of equipment. My boots for exemple, are from Lowa, they only make boots since the 30s. My EDC knife is a Spyderco, they only make knives (and a very innovative company BTW, from an innovative nation that others mimic without being really conscious most of the time), I'm looking at Ray-Ban or American Optical Eyewear for good sunglasses and at Hamilton for good mechanical watches. And I can afford the Tilley given it's an essential item. But I must be honest, it's just the look that I find not very appealing.
Frankie