You can get cheap LED lamps that clip onto the underside of the brim of a cap, as well - so you can wear your favourite branded sports/shooting cap with the same "benefit".
For my own part, I'm not likely to be wearing a hat designed to keep the sun out of my eyes at the hour of night when a lamp would be required.
I'm more likely to be wearing a balaclava or similar, so my preference is one of those LED lamps on an elastic headband - also hands-free.
With the advent of inexpensive LED lamps, I have replaced nearly all incandescent lamps in my camping/survival kits with LED equivalents. They consume far less power and the LEDs are more robust and have longer lives than incandescent bulbs. Everything that used a standard cheap incandescent bulb is obsolete.