The first wig cap I bought was great to wear. Since it has to be washed from time to time, I got some more, but they are a lot tighter, and can give me headaches. Getting the right size seems to be important, and I am not sure how one does that when the are allegedly "one size fits all". Getting the front of the cap high enough, as Michelle said, is important. It is also important to make sure there are no wrinkles in the band.
Yes, I do wear a hat instead of a wig on occasion. It has to be an event where I will not need to remove the hat. For dog-walking, I wear a wide-brimmed sun hat, or a ball cap. I went to one outdoor winter event last year where I wore a knitted tuque over my own hair. I keep my own hair short enough to tuck under a wig, but long enough to show some curls from under a hat.