The oldest hen will probably taste the strongest, if that's what you're after. I do not believe that one breed necessarily tests better than any other, but the age of the chicken does make a difference. But with age comes tough and stringy meat. So, it's always a trade-off between flavor and texture.
For all intents and purposes, there is one type of "meat chicken", often called a cornish cross. There are various varieties of the cornish cross, created by various breeders at various times, but the differences between them are minute.
Then you have the heritage breeds, which grow much slower and offer less meat, but some folks here swear by them. Likewise, you can eat an old hen, but I wouldn't try frying or roasting it.
Somewhere in the middle, but leaning heavily toward "meat bird" are the "Freedom Rangers". These offer a balance between slow growth and pounds of meat. I believe that these taste a bit better than the cornish cross, but it's not a huge difference. Additionally, they forage more than a cornish cross and are generally more active birds, but not as active as any heritage breed, and not as good at foraging, either.