Hey Aussiegirl, your grandmother may not have been refering to the Cornish Cross when talking about the taste of free-ranging birds. From what I understand, at least in the US, the Cornish Cross only started becoming dominant in the 1960s. In part because heritage birds are generally left to age much longer, the taste of a free-range Cornish X may not compare with that of other meat birds.
I recently had the oportunity to try a free-ranged Cornish X from a local farming family. The texture was (in my opinion, far superior) firmer, and the body looked a bit healthier without the excessive fat globules I have to cut off store bought birds. That said, the taste was exactly the same to me, and the dark meat sections were still almost as pale as the breast meat, just as it is in store bought. It was slightly less slimy though (again, improved texture). The dark meat in heritage birds, if you've ever seen photos or the real thing, can be almost purple in color! This particular bird was killed when fairly young and small. Some people who free range their Cornish Xs let them grow out to an older age, so I suspect they would have more flavor in addition to improved texture. But, I've heard from other people that they were disapointed to find that while they also ended up with improved texture and less fat grossness, that the actual flavor of the birds was the same as a higher quality store bought bird. These same people raved about the flavor of heritage birds.
I just put in an order for a Freedom Ranger from the same family, and they are supposed to be sort of a halfway point in taste, etc. between the Cornish X and heritage birds. Towards the end of October, the same family will have Naked Necks available, and I will again compare the taste. Those should be noticeably more flavorful and firmer from what I've read. I'll post about it when I've had all three to compare. Hope you can find a way to compare birds as well to see what you like best!