I don't know that trash fish is the right word to describe common carp but, they certainly aren't high on most peoples most sought after game fish list.
As to eating quality goes, I understand that some people like carp but most people don't find the taste all that palatable. I am not the only one who holds that view. I was reading MO Conservation Magazine a few months ago and they stated that common carp have to strong of a flavor for most peoples taste.
The thing I have against carp is that they are way under fished. They, and bighead carp, soak up way to much of the available biomass in our rivers, stream, and lakes, again this is per MO Conservation Magazine.
I would love to see them become a viable sport fish. If they were to be pursued more the numbers would decline, there would be more room for the remaining Carp to attain trophy size and it would help take some of the pressure off the natural habitat of other fish.
Another problem, again according to MO Conservation Magazine, common carp have a bad habit of wallowing and therefore destroy vital habitat for bugs and micro-organisms that other fish use as food. Carp are the biggest shufflers of the fish world.
As to comparing them to Trout, Brown or Rainbow, there is no comparison at least in the Ozarks. They can't survive outside the cold water areas they are stocked in.
Right now I see common and bighead carp as the Starlings or English Sparrows of our lakes and streams. They are invasive, over populated and destroy biomass vital to other fishes survival. Something needs to be done to lessen the impact they are making on our lakes and streams.
Seems to me if people in other countries like them so well we could net about a billion pounds and ship them to starving people in Africa or North Korea or wherever.
JMO which I know isn't worth much.