For native speakers who are good at math (Engineer, physics major, math major) then the GMAT is way better in my opinion. There's no vocabulary tested on there, Thank God, but instead your logic/reasoning is what really matters. But it takes way longer to prepare for the GMAT. I studied for 5 days for the GRE simply by doing a couple practice tests just to make sure I'd get a perfect in math (verbal doesn't matter for engineering grad school). I didn't do so well in the verbal section but a big part may have been that it had zero effect on my engineering grad school chances once it's above 500.
So yeah, for a month of studying you're better off with the GRE unless your vocabulary is atrocious. I know They've changed the format of the GRE (I took it summer of 2010) and I don't know how if the change was significant verbal-wise.
Just realized that you only need a 600 on the GMAT. Why don't you just look study the exam's format for a day then download the free gmatprep software from mba.com and look at your diagnostic score. Native and good at math will definitely put u above 600 without any studying. So I take back everything I just said haha