From what I understand, this is what carrots often looked like originally. It was later on that we selected for more orange carrots.

Either way, they certainly don't taste beetroot-y. I've heard them described as somewhat sweeter. I've had them only once so far, but would agree with that description in the sense that they have a more rounded taste. I think, I like their taste slightly more.
Wikipedia also says that the orange carrots probably won out not for tasting better, but rather because they don't discolor stews, which is a fair reason.