As a Cross Check owner, I occasionally get a little tired of the endless LHT partisanship.
The LHT is optimized specifically for touring; the CC is a little more versatile of a bike. If you're only touring occasionally, it may be a better choice.
I don't think the differences are all that significant; the main one for you is just going to be heel clearance. If you're using smaller bags, that may not be a problem at all, but it is one you should check on with your LBS before committing to one bike or the other.
The main thing to watch for if you get a Cross Check is to get them to lower the gearing, e.g. configure it as a triple or compact double rather than a standard double. Any decent LBS will set it up that way without charging you extra.