Keep in mind that many regional flights are operated by companies other than the mainline under contract. A few of the regionals are owned by the mainline but most are not.
A meaningless distinction for members of the traveling public.
I'm a member of the traveling public and I find the difference between mainline and regional service to be night and day. Nearly every trip I take is routed so that it utilizes mainline flights as much as possible. Cramped seats and limited service regional jets flown with overworked and undertrained staff employed by regional carriers with lax standards and poor safety records is not my idea of a good time.
Kudos to you for being an informed traveler.
I think a lot of people know the difference between a large plane and a small plane, but I suspect the vast majority neither know nor care whether the flight is technically operated by Delta/AA/United or Air Wisconsin/Chatauqua/Compass etc. The parent carriers market the flights as being their own, right up until the moment something goes wrong, in which case it's "don't blame US..."