I have about 20 dark cornish hens and a couple roos for breeding. I've only eaten one rooster. The meat tastes like chicken to me. No different really from any other farm raised bird. The shape of the body is what's different. The breast is much wider and long. It's not as thick as the cornish cross, but you get more breast meat off one than you would a rooster of another breed.
I really like the hens. They are great foragers. They fly over the electric netting every day to go 'hunting'. They are definitely the most active birds I have. They look a bit like tiny haws with their feet set so far apart.
If you want a "cornish game hen" raise a dark cornish or a cornish cross to 3 lbs live weight and there you go.
If you are serious about developing your own meat birds, then cross your cornish (good luck finding a white cornish, though) on your Plymouth Rocks, Sussex, RIR's, or whatever you hvae available. The hybrid will be better than any pure breed alone.