I've shopped insurance in the past. There wasn't much of a difference in price. Of course, I was only sticking with 3 of the major players. I never even considered the random off brand insurance company. I'd rather pay more with a big player and have the company actually insure my stuff if or when the time comes. Never had a problem either geico or nationwide.
I was in a fender bender approx 2 years ago. Other parties fault, minimal damage. They had some fly by night insurance. Took months to get the $500 check from them. It was nearly impossible to speak with someone. It was bad. After that experience I said I would never use a company like this to insure anything of mine.