elementary does not have a minimal install option due to the fact it is pretty light in the first place.
The minimal option in Ubuntu removes things like LibreOffice, Transmission, etc... that can get pretty large and not all users want. As far as I know, it's mainly for saving disk space, and probably doesn't offer much if anything in terms of performance gains.
There are only a couple of pre-installed applications in elementary that run in the background (and hence possibly have an impact on performance). These are namely AppCenter and Calendar. Keep in mind that if you remove the autostarts for those or remove them completely, you won't get software update notifcations or calendar notifications respectively.
Pretty much everything else starts and closes on demand so they'll only have an impact on system resources if you explicitly launch them and leave them running.
Anything else that's left running after that is pretty much a required component of the session. You could experiment with stripping things out a bit more, but it would be likely to cause issues.
Edit: Also worth adding that latency for audio production is more likely to be affected by kernel things like the scheduler and various drivers etc... than it is the applications that are running. I know Ubuntu provides low latency kernels in the repository but I have never experimented with them or know whether they work with elementary. Just bear in mind that unless you're using the exact same kernel in two different distros, it's probably not a fair comparison.