I'd definitely find a way to try before you buy.

The LHT will put you in a more upright riding position with the taller headtube and additional 10 degrees of rise in the OEM stem, and the longer wheelbase makes it feel like driving a '72 Cadillac.

Beyond that, with the complete bikes the CC has better brakes and bars (at least IMO). The LHT has a better rear derailleur, hubs, tires suited for pavement, 36H rims (may or may not be a good thing), and a wider gearing range with the triple and 11-34 cassette(also may or may not be a good thing). Of course, any of these components should be able to be swapped at time of purchase, but the OP wanted a complete bike and these are some of the component differences in the complete builds.

Edit- might want to check out http://groups.google.com/group/surlylht and see if there are any CC or LHT owners that might let you take a test ride.