ROCK may not run on a Mac Mini (even an Intel one) or not easily as it probably doesn’t have the drivers, but you might get around that e.g. with a an external USB ethernet dongle like here:
or here:
However:
- It will be unsupported
- Open Core Patcher does not come into this because ROCK is an operating system and replaces the macOS
On the other hand, ROCK is not supported on a Gigabyte Mini PC either. You’d have to try with either if it works.
I guess it comes down to which one has the faster CPU and that’s clearly the i5-4278U. (Though the i3 uses less power if you care about that). Also depends on your library size
https://www.cpu-monkey.com/en/compare_cpu-intel_core_i5_4278u-vs-intel_core_i3_4010u