The Tricross has avid bb7 disc brakes, a better seatpost. But it also has an aluminum fork whereas the Giant has a carbon fiber fork. The giant is a better value because of its components but that doesn't mean its a better ride. Also be aware of the different gearing, the tricross has a typical compact setup(50/34) whereas the Giant has a cyclocross setup (46/38).
Earlier this year I test rode both a tricross and a gaint tcx1 (both were 2012 models), and I found the Giant to be a very uncomfortable ride an much prefered the ride quality of the tricross. However in the end I bought a 2012 Specialized Crux disc. The Crux is Specialized's true cyclcocross model while the tricross is billed as an all purpose bike.
Hope all that is helpful and good luck making your decision.