The Tiagra RD on the Fuji is the older 9 speed Tiagra. Looking at the specs, the GT has a better group, the Fuji has better wheels. The other difference is that the GTR frames have a fairly aggressive geometry, and the Fuji is endurance geometry.
After I responded before, I saw another thread on GT with a link to their 2014 model line. Seems like they've downgraded the components since 2012. The 2014 series 3 uses a mix of Sora, Microshift, and Sun Race components. So I would definitely lean towards the 2013 with full Tiagra, if you decide on the GT.
I think what you need to decide on first is whether you want a more endurance geometry frame, or a semi-aggressive, more race oriented one. The GTR 3-5 frames aren't as aggressive as some race bikes, but they are more aggressive that the Fuji. Most entry level aluminum bikes will have similar component groups, and Sora works well enough for new riders. Most will also have entry level wheels, but Jalcos were the worst wheels that I ever owned.