Yup, as alterego said, it depends on where u r strong.

Quantitative seems to be similar in GRE or GMAT. Reading passage is similar, Writing assessment is also similar.
The deciding factor is VERBAL section. (Antonym, analogies, sentence completion in GRE Vs Sentence Correction, Critical reasoning in GMAT)

In GRE if you could memorize maximum possible word meanings from different books, it is likely that you do very good in exam.

In GMAT, you need to be very good in grammar and critical reasoning which I believe is pretty hard than GRE at least for me.
So it depends on how ur english background is.

If I were in your position I would go for GRE. I do not have strong background in English but at least i can try memorizing those word meaning even if I do not know how to use them, at least i can do good in antonyms, sentence completion and analogies. But I cannot
improve in grammar much than what I learned in my school time in this limited
time frame.

The best is take at least one GRE and GMAT exam online, find out the difficulty you can decide whether you can improve grammar and reasoning for GMAT or go to memorize word meaning for GRE.
I prefer Barron's book for reading, however for exam practice, I prefer Kaplan's CD.