A Trek 520 will get you across the US just fine. The Giant would likely do the same. Looking at the Giant for the first time, I am surprised to see disk brakes. I have had problems with cantilever brakes before (very fast downhill full load emergency stops in the rain) and I hope to be experimenting with discs latter this year. One possible problem I see with the discs is interefence with racks and bags.
The compact design of the Giant may also make fitting rear racks difficult, but the standover height from the compact design would be nice when you have a tall load on back and cn't swing your leg over normally. The Trek comes, or at least it came, with barend shifters. These are theoretically more reliable than the STI sh*ters on the Giant, but in actual use it is not an issue.
One other thing I notice about the Giant is the Integrated headset. Touring bike when properly loaded (lots of weight in the front panniers) generate a lot more force that must be taken up by the headset. It is very easy to damage an improperly adjusted headset. With the Trek, this means a new headset, but the Giant may require a new frame.
The gearing on both is the same and I have no issues with it, maybe that's why I had brake problems before. Try out both bikes and see which one fits you better. If possible, ride them with full loads because they will handle much differently loaded and unloaded. Personally, I don't like the handling of my Trek unloaded, but it's perfect when loaded. I'd say get the one that fits best, and I'd lean towards the Trek in a tie-breaker.