Hello Alinne,
Here are a couple of articles:
It's not necessarily an easy question to answer, as the effect size can vary depending upon what you are studying (e.g., it's large in IBD studies, whereas for a category like gender differences, it's quite small).
You may also want to consider how diverse a community is, e.g., many insect guts are not diverse (so you can feel more confident about capturing rare taxa with lower sequencing counts) whereas soil samples are incredibly diverse, so if you are concerned about differences in rare taxa, deep sequencing would be preferred.
Hope this helps,
Tony