As today (BTW happy new year) the BS DO NOT have any preference and DO NOT have any bias to accept both. This is a fact now. And cannot be reverted.
The myth of GMAT over the GRE is a thing that held back 5 or 6 years ago no more in 2020.
Moreover, these are the two main differences between the test and what they have in common
1) GMAT is specifically made as a test for Business School; instead, GRE is perfectly fine for the Business School (above 80% percentile, of course, which is roughly 700 on the GMAT scale) but it is also suitable for a variety of fields of study, ranging from art to psychology.
2) GMAT basically is a quant test. However, the GRE is much harder on the verbal side.
Common ground
1) RC, CR, and PS are THE SAME. Same concepts, same the skills you do need to tackle the questions. I shall not delve specifically into the areas tested which are a bit shifted and do not completely overlap.
2) Both the exams account for roughly 20/25% of your ENTIRE application (SOP, LOR, so forth). Students on getting this point are really, repeatedly stubborn. I do not know what is difficult about this pivotal concept.
The GMAT and GRE are only a piece of the entire puzzle and they do not account for either for the majority. I think I'll die on this board and still, I shall hear the students saying: ok I have 720 on the GMAT and done: I am already into Columbia BS.
Here my guide about the GRE and the score you do need for the BS
The GRE average score at Top 25 Business Schools 2020 Ed.