Most people really don't won't to know whether they SHOULD take the GMAT or the GRE. The real question they are often trying to answer is "which test is easier the GMAT or the GRE?" The short answer is, "the GRE" as explained in the article
Which is easier- the GMAT or the New GRE?
However, if you want to know more about the differences between the two tests keep reading.
Target School
You should start by writing an e-mail to your target school and asking if they have a preference. For many MBA programs (about 1/3) the GMAT is still the preferred test. However, that makes about 2/3 of MBA programs that are indifferent. If you applying to a different masters program or a doctorate program schools it's more likely that the school will have a preference.
General
1) If you know which schools you want to apply to first see which test(s) they accept and which test they prefer.
2) G.R.E. is less expensive ($140 in the US and $180 in Europe) than the GMAT ($250)
3) Many people do worse on the GMAT math when they first take a practice test because most people have never encountered a data sufficiency problem which takes some getting used to.
4) TIME. The GRE is about an hour shorter than the GMAT; therefore, stamina isn't as much of an issue on the GRE. This factor should not be overlooked because many of the mistakes that people make on the GMAT are caused by lack of concentration, which in turn is often caused by lack of stamina.
Verbal
The GRE uses questions that require a much larger vocabulary than the GMAT.
The GMAT has a grammar section that the GRE doesn't have. In this section you are given a sentence and asked to correct it.
The GMAT has logic questions that are not on the GRE. In general this sections tests your ability in argument constrution, argument evaluation, and formulating and evaluating a plan of action.
Conclusion- if you’re really good at vocabulary or learning vocabulary, or if you’re not very good with American English Grammar you should consider taking the GRE. Otherwise, the GMAT might be more for you.
Writing
The GRE issue essay is fifteen minutes longer than the GMAT issue essay. The GRE issue essay also gives you the choice between two different issue prompts whereas the GMAT only gives you one.
Conclusion- Some people get stuck if they only have one choice to talk about. If you think you’ll need a second option for the issue essay the GRE is preferable. However, if you don’t have trouble thinking and writing about most subjects it might be to you advantage to take the GMAT because there will probably be some people that will get stuck and this will make your percentile rank increase.
Math
Both the GRE and GMAT test approximately the same basic math concepts, but in general, it is easier to get a higher composite score (the score that is out of 800) in the GRE math section. Admission committees know this so they mostly look at your percentile rank and not your composite score. However, if you only need a high composite score the GRE might be easier for you.
In general people have a harder time with the GMAT data sufficiency questions than the math problems on the GRE since the question is posed in a way that 99.9% of people have never seen before. As with all math questions, however, practice will make you better.
The data interpretation problems on the GRE are harder since they often combine multiple charts and/or graphs at the same time.
GRE Quantitative comparison questions can be done faster than any other type of math question, but they also tend to be trickier so if you don’t see the trick it’s easy to get them wrong.
Conclusion- If you only need to get a certain composite score on the math section to satisfy a school’s requirements then take the GRE. However, the difficulty of getting a good percentile rank (85th percentile for example) is almost equal. If you only need to get around the 70th percentile though the GRE is probably easier because you have a lot of applicants who take the GRE and who don't care about one of the sections. For example, a person who is applying to a PhD in English won't care about the math section, and because there are many people like this, it's easier to get a middle level GRE score.
A good indicator
One thing you can do is take a practice test of each and compare your scores. Use ONLY official tests (since other tests may be inaccurate), which you can download for free from here:
Remember though, Data sufficiency problems have a definite learning curve so don’t be scared away from the GMAT just because you didn’t do well on them. If time is a factor (as it usually is) one of the big questions is whether or not you can learn vocabulary (a couple thousand words) or grammar faster (a couple hundred rules).
For more information or to make an appointment for a GMAT / GRE tutor in Paris
Contact: Dan at Dan.GMAT.GRE@gmail.com