You can eat any chicken of any age, sex, and type but there are trade-offs. The Cornish X broilers are bred to grow big and fast, to be very efficient in converting feed to meat. The Ranger types are similar but not as fast or efficient. The dual purpose types like RIR's grow a lot slower. The egg-laying types like leghorns will never have much meat on them. Then you go down to the bantams. They can all be eaten but there are differences.
In my opinion the big differences in texture and flavor in the Cornish X broilers and the Dual Purpose chickens is that you typically butcher the DP at different ages. The CX are typically butchered at 6 to 8 weeks old. At this time they are extremely tender and with not much flavor. If you butcher a DP at the same age they would be equally tender and bland, but you'd have trouble finding much meat, even if fed them like CX broilers.
Lots of us raise DP chickens for meat but we wait to butcher them so there will be some meat on those bones. The older they get the more texture they develop. At a certain point you have to alter the way you cook them or they become too tough to eat. You can fry or grill a pretty young bird but if you try that with an older bird you can wind up with shoe leather. There are all kinds of ways to cook chicken, fry, grill, roast, bake, smoke, stew, crock pot, pressure cooker, and so in. In general the older the bird the more it needs to be cooked slow and moist. That's about texture.
Then you have flavor. The older the bird gets the more flavor it develops. Some people like that, some don't. We all have our own preferences. With females this change is relatively slow but when a cockerel hits puberty and this hormones kick in the flavor change happens quickly. Some people describe this as a "gamey" flavor.
Your question was specifically on taste. Yes, there is a difference in both texture and flavor if you wait to butcher them until they have meat on them. Texture you can handle by how you cook them. Flavor is more of an individual thing.