Basically same phone, but better camera on technically faster SoC in the G. The Tegra is no slouch, and it does have optimized software for it (the Tegrazone stuff), while the Snapdragon will be a screamer but have a lot of unused performance potential.
The camera might be the biggger deal, with many people saying not so good things about the 4X camera compared to other superphones like the One X and S3. The G is supposed to have a REALLY good camera. Both screens are really good, from what I've heard from people that have seen them.