elPatron434Before I post anything, I want to clarify that I've never taken the GRE, nor have I read any concrete research proving that the AdComs view one of these two tests as better. Most of what I'll write next is based on secondary research and anecdotal evidence, and in the end, it may not be radically new advice.
To begin with, GMAT is a test specifically for business/management graduates, whereas GRE is designed for any graduate program applicant. As such, I believe the signal sent by a great GMAT score would be stronger than that sent by an equally great GRE score.
There's a certain availability bias in favor of GMAT scores, which I'm sure you have also noticed in your research. More people applying to business schools take GMAT (85-90% admits at any T15 school submit GMAT scores, if not more), and it is easier for anyone, including AdComs, to compare apples to apples than to compare apples to oranges. I think ETS provides a GRE to GMAT score converter, but they don't really share the methodology in detail, so it's a bit murky. I'm not really sure if AdComs would put the time and effort to convert GMAT scores for every applicant who submits a GRE score; they'll mostly go by some arbitrary rubric and some mental math. As an applicant, that's a territory you want to avoid - where the AdCom makes some assumptions about any part of your application.
Moreover, both ranking publications and recruiters prefer to see GMAT for their respective purposes. This, in turn, creates an initiative (if not incentive) for AdComs to lean more towards seeing a GMAT score in the application vs. a GRE score. GMATNinja mentioned how, for example, there could be an incentive for AdComs to prefer GMAT (for both admission and scholarship considerations) because of the correlation between GMAT averages and school rankings, and from my experience, I've realized that the entire admissions process is a very fine dance of negotiation between what you get from the school and how you can contribute to the school's benefit. A higher-than-the-school-average GMAT score is definitely one of those ways. Did I mention employers prefer GMAT? It's anecdotal, but in consulting, some employers really nudge students to submit GMAT scores.
From my observations, I have seen more Indians with GMAT (and 740+ GMAT) get more scholarships. But I think that's more to do with the fact that more people submit GMAT scores, to begin with. Would those people get the same scholarships had they submitted an equivalent GRE score? We do not know. A test score can influence your scholarship dollars but it's not the only factor; the real factor is what do you bring to the table overall and how you can contribute to the school and its community, both as a student and as an alumnus.
With COVID, one thing that we never expected to happen (amongst 1000 others) is that so many schools, including some of the most elite institutions, are willing to consider applications without a GMAT OR GRE. To me, that shows flexibility and that schools have a backup plan to evaluate whatever skills they were using the test scores to evaluate. Not sure if this trend will continue in the next application cycle, but perhaps you could connect with an AdCom at one of your target schools and ask them how are they going about evaluating applicants sans a standardized test score. You may not get a super clear response, but you may get something.
Overall, if you feel that you can score well on the GMAT (in your case as an Indian engineer male, "well" means 740+), then go for GMAT. Otherwise, submitting a great GRE score is any day better than submitting a crappy GMAT score. Hope this was somewhat helpful!