System resources used when using Elixir with MySQL vs PostgreSQL

Until you grow to the size, where you will be able to hire someone to handle that for you, then you will probably do not see any difference.

It is hard to tell what will work better in your particular use case, so you will need to do benchmarking on your own. However I think that you will still see no difference, and if so, it will be indistinguishable from noise.