The gain dial on the H6 with the NTG2 is on 4/5 on the Zoom Shotgun its on 9. The noise floor on the NTG2 is much lower and the recording is a lot cleaner you don't have to boost it any where as much.
what mice are you comparing the NTG2 to? it is a directional mic and can only be compared to other shotgun mics.
Sure its not as sensitive as an NTG3, but hey if you want to spend $600 I think thats a whole new ball game.