I own both and they are my primary scopes on my two primary rifles (diff calibers). I often shoot them back to back (waiting for barrels to cool). Please note that these are only representative of one example of each.
If you're nitpicking and look closely at distance (anywhere past 600), the AMG is noticeably better in the resolution department.
The g2r is noticeably better than the AMG in terms of eyebox size/ease of getting a clean sight picture IMO. You'll get it as normally as you would any other scope on the AMG (good actually), but the g2r is practically a heads up display for the magnification you're getting. Helps during positional shooting.
With the difference in objective size (25% more glass on the g2r), the brightness is not as pronounced as you might think, that is one area Vortex really did some magic with the AMG (though Kahles 624i is brighter IME, while the AMG resolves slightly better).
I think the FOV is slightly larger with the g2r, but only slightly. I recall doing the math in another thread and they were almost identical. Maybe the magnification markings on my scopes are off, but at the same mag the g2r FOV looks slightly wider... barely worth mentioning.
The reticles are both very good. The AMG reticle is designed for PRS competition IMO (ie. movers), with the center floating crosshairs a nod to hunting usage. If you require .2 spacing, it's your reticle. If you like an open center and prefer a very usable but cleaner reticle, the g2r reticle is your reticle. They're both very good and it's just personal preference. I prefer the cleaner g2r EBR-2C myself.
For the greater eyebox flexibility (which I value highly on my list of priorities) & reticle, I prefer the g2r overall between the two even though the AMG resolves better.
If weight is an issue, consider the AMG or Kahles 624i. If not, the g2r is an amazing optic in its price point and would be my recommendation over the AMG for general shooting. g2r also has greater elevation if you shoot ELR.
Compared them again side by side. g2r has more color pop, AMG has better resolution