The test score is one of the objective parts of the application and on which you are supposed to have some command. A better score is definitely going to help, no guesses there.
So which one should one choose? Well it depends; let me summarize:
GMAT: If you feel test score will be one of your strengths; as in you are from mid-level college/ less research exposure etc. and you could do well in either test choose GMAT
GRE: Schools want their average GMAT to go up, as it gets counted in rankings. So in case you feel you would fall below average, go for GRE
In short, GMAT could be a feather in your cap or a bad criminal record and GRE could be just neutral information. So choose GMAT, if you could break school’s average. Amongst the two section, the quant percentile is more weighted compared to other segments for admissions. Therefore, if you have more than one score, submit the one with a higher quant score if the difference in total is not significant.

Unfortunately, PhD admission’s score requirements are relatively higher than that of MBA’s. Therefore, in case you couldn’t get average info, add 20 to MBA’s average. Normally, it’s somewhere between 680 (~rank 70) to 740 (top 20). One more caveat, you might get some respite or aggravation depending upon the concentration you choose. Following is the score reported on Moore School website for 2015 admits:

Concentrations Average GMAT Difference
Accounting 703 13
Finance 724 34
International Business 693 3
International Finance 700 10
Management 681 -9
Management Science 647 -43
Marketing 679 -11
Total Average 690

Therefore, if a particular school, let’s say Olin School, gives you 720 as the average GMAT Score; and you are applying for Marketing then for you the average is 710.

One caveat here: some schools state their preferences in the application requirements. Some programs, such as Kellogg Finance program, say they prefer GRE but accept GMAT.  Many programs prefers the other way round. So you could also pick one over the other based on your college selection.

However, I would like to stress that these scores are neither deal maker nor breaker. Average scores across years vary dramatically across years, indicating preference of research fit/ profile/ publication over final scores. As such, do reach out to colleges with averages much higher than yours, if you feel engaged in the research being done there. For GMAT/ GRE preparation begin with official books and proceed to information on the web.

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