My own observations over the years have determined for me AAF heavy bomber pilots were more partial toward the dress cap, or "50-mission crush" cap, so called because it had been pushed together on the sides and shoved in a handy recess in the cockpit during flight, or sometimes worn on the head during flight. It was common practice for AAF "heavy" pilots to remove the wire grommet that went around the inside of the cap, stiffening it - the excuse was so that it could be worn on duty while placing headphones over it, the real reason was because it looked "cool." The second choice was the "overseas" cap, the "fore and aft" cap, because it could be easily folded into a flight suit pocket or left on the head, headphones placed over it. This was because many ground officers at AAF airfields they might drop into would give them hell for not having headgear once they were on the ground and outside the airplane; hence they carried this cap for ease of carry and its ability to be donned quickly. This tradition carries on in the USAF today. Other than that I don't think any other kind of headgear was popular for the bomber pilots than the flying helmet, leather or cloth (later in the war). It had the advantage of helping to keep the head warm, but was not as stylish as the other two caps already mentioned. Fighter pilots wore the leather or cloth flying helmet. I've only seen a couple of photos of pilots in BT-13s wearing 50-mission hats, I don't think a student would have the nerve to do this unless they were airborne and away from the airfield! Some guys (frequently transport pilots) also flew with nothing at all on their heads, but I don't think this would be advisable in a combat area. I'm a long-time student of the AAF and this is what I've noted in various photos of the service over time.
Navy aircrew had an assortment of headgear to wear, but many of them, officer & enlisted, used the ball cap as most of their flying was in temperate or tropical areas and this was better suited to shielding the head from the sun and aiding visibility as well. The other thing I've seen them wear in photos was the flying helmet. I've also seen photos of PBY gunners wearing their "dixie cups" while on the guns - sometimes the headgear was dyed dark blue.
this is how i'd imagine a Harpoon crew would look for their 'crew photo'
Yank those hats off boys! LOL