My experience of taking a GRE practice test while I've always been studying for GMAT:
I've been studying for GMAT so far, and my score is around 720-730 (Q50, V37-38). Yesterday I went to GRE website and took one of their practice tests (they have two free tests). This was my first GRE experience. I skipped the two writing parts and directly went to the Verbal and Quant.
I found GRE's Quant much easier than GMAT's. Surprisingly, I got all 40 Quant questions correct without any timing problem (this has never ever happened to me in GMAT that I can get all 31 questions correct on time, I usually have at least a few questions wrong). The GRE software gave me a Quant score of 170.
GMAT quant questions are overall are trickier than GRE's and it's much easier to make mistakes in GMAT. While GRE's questions were more superficial and not as deep in terms of content or hiding something that makes you get something wrong. I'd say the hardest Q questions that I saw in this practice test were in the range of 680-720 in GMAT quant. So imo if everyone is thinking about switching to GRE, you will be just fine and even better off in Quant if you have been preparing for GMAT.
The problem, however, with GRE, at least for me, was their verbal vocabulary questions. I got virtually all vocab questions wrong!! My score was 152 in verbal, which is much lower in terms of percentile compared to 37-38 of GMAT.
The GRE verbal I'd say has three parts: RC, which was similar to GMAT's RC. CR, which was easier than GMAT CR. And Vocab questions, which I found them very hard as someone who has never studied this sort of high level English vocab. The vocabs are much more advanced than what we usually see in the RC, books, news like NY, economist, etc.
So in summary, I'd say the only noticeable difference between GMAT and GRE is vocab questions. In quant section you will do just fine. I'd say if you've been scoring 48-51 in GMAT quant, there is a high chance that you will get a perfect 170 in GRE quant. Those muscles that you've built for GMAT Quant will easily smash the GRE questions.
As for verbal, RC and CR are the same. There is no SC in GRE. Instead you will have a bunch of vocab questions. If english is your first language or if you think you're good in this part, don't hesitate to try to take a GRE test. You may perform even better in GRE overall.
As for me, since I don't have time to start reading the vocab, I'm gonna just stick to GMAT and wait until centers are open and then I will take a GMAT. I think my 720-730 GMAT would probably be better than a 322 in GRE.