Most business schools now accept both the GMAT and the GRE and state emphatically that they do not have a preference for either test. In 2009, when a few schools started accepting the GRE -- Harvard was among the first -- many other schools, such as the University of Chicago, declared that they had no plans to follow suit. However, such schools soon realized that accepting the GRE encouraged applications from a wider variety of non-traditional business students -- those with undergrad degrees in the social sciences or engineering, for example -- thereby giving schools the diversity they seek in their student body. This is because many students with non-business undergrad degrees are undecided about what graduate degree they want to pursue, and taking the GRE gives them more choices.
The GMAT has been the primary test for prospective MBAs for many years, so admissions directors are familiar with it. They trust the test and understand it well. Applicants with business, finance, accounting and other quantitative backgrounds should take the GMAT because they will be compared against others with similar backgrounds, who will be taking the GMAT. However, getting a good score is the most important point. Test takers who don't do well on the data analysis questions when preparing for the GMAT might do well taking the GRE instead because it doesn't have these questions.
Anyone considering several graduate school options in addition to the MBA program can usually take just the GRE and satisfy admissions requirements for nearly all graduate schools. Both tests require advance preparation and taking practice tests, so it's a plus to put all efforts into just one test. Candidates who aren't as strong in math may perform better on the GRE, which some consider to be an easier test, at least in the quantitative sections. However, they'll be compared with arts and sciences students -- the bulk of those taking the GRE -- who may score very well on the verbal section. Admissions committees like to see strong, fairly even scores in both areas, so students who opt for the GRE should be confident that they will earn a high combined score.
Before deciding to take the GRE instead of the GMAT, candidates should consult the websites of the business schools they're considering. A few schools still do not accept the GRE. For example, UC Berkley only accepts the GRE for part-time students. UCLA will accept the GRE, but states on its website that they "strongly prefer" the GMAT. Admissions requirements can change at any time, too, so even schools that currently accept either test without preference may decide to drop the GRE.