It kind of depends on what you prefer. My friend has a CC that he uses mainly for commute. He's done a little bit of touring. It's good enough for shorter tours, however, if done right, I'm sure you could bike across a state on a CC and have enough room for all your gear. The LHT would just be more convenient.

Personally, if given the choice, I think I would go with the CC. I like something faster and don't ever plan on going on week long tours.

Whichever one you pick, I don't think you can go wrong.