That depends strongly on the dealer and region, in my experience. When I lived near my dealer I always took my vehicle there, because routine maintenance and even new tires were either less expensive than or approximately the same in cost as prices at local mechanics I researched.
The only reason I don't use a dealer now is because I found a fantastic actually-small-business mechanic who is closer to me, and who didn't try to pull the wool over my eyes and whose prices are reasonable.
Depending on the repair, I may be more than willing to pay extra. New tires for my '84 pickup? Sure, I can go anywhere. Overhauling the engine on a turbocharged BMW? Yeah, I'm going to want expertise & factory parts.
The only reason I don't use a dealer now is because I found a fantastic actually-small-business mechanic who is closer to me, and who didn't try to pull the wool over my eyes and whose prices are reasonable.