my neurologist put the nix on ballcaps for me...or anything that constricts my head. When you exercise, if your helmet (or ballcap) is too tight, it may get even tighter, or constrict the flow of blood.
I am picky about my bike and riding helmet...I have a very nice (and expensive) Specialized helmet...for me, it fit the very best, and is very adjustable, and doesn't squeeze my head. I have a less expensive but irritatingly poor fitting helmet for my MTB...I am never on it for the extended periods of time I like I am on my RB...but the times I have worn the MTB helmet on my RB, it has given me a headache.
Go for something with a broad sweatband...