I have taken both the GMAT and the GRE and these are my scores:

GMAT 680 (Q43, V40)
GRE 166 Quant, 164 Verbal

Which one should I submit when I apply to MBA programs? I know that business schools prefer the GMAT but my GRE score converts a bit better.

This depends on your goals. Take a look at
- GMAT Tiers - strong schools for your GMAT www.find-mba.com/board/27082
- How to use LinkedIn to find the best school www.find-mba.com/board/33571
- https://find-mba.com/board/general-forum/is-there-an-efficient-frontier-in-mba-selection-45894?

You can often submit both scores. What schools are you applying to?

I'm applying to USC, Ross, and Scheller.

Definitely the GRE. This table is helpful. https://poetsandquants.com/2018/04/12/average-gre-scores-for-top-mba-programs/3/
I will say, that many/most admitted GRE candidates are diverse in some way, so these stats might not apply to you but it gives you some idea. They are becoming more and more receptive to the GRE with each passing year; they are able to see how well it predicts classroom success.

I have taken both the GMAT and the GRE and these are my scores:

GMAT 680 (Q43, V40)
GRE 166 Quant, 164 Verbal

Which one should I submit when I apply to MBA programs? I know that business schools prefer the GMAT but my GRE score converts a bit better.

The scores are close enough that I would just send both. If anything, it shows that your test-taking performance is relatively consistent, and since these two tests address different qualities to some degree, they would look at you at a pretty well-balanced candidate.