The Cross Comp is a cyclocross bike, so some of the components will not or might not transfer directly. First, you will need to replace the Fuji's linear-pull brake calipers with road-style calipers, preferably of a dual pivot design. Second, the Fuji's tires, and possibly the wheels, will be too wide for the Giant's tight clearances. Third, you may eventually want to replace the Fuji's cyclocross crankset with a standard or compact road setup. Seatpost diameters and front derailleur attachment might also present some incompatibilities.

That said, I love my older TCR C0. It's not a bike to fall asleep on, but I can ride it hard all day.