Are you staying in the ecosystem? Like Intel to Intel or AMD to AMD? If so, you're probably fine outside of any motherboard BIOS changes you may have made(those would need to be changed again on the new motherboard).
Personally, I've never had any issues with just keeping the same OS install on whatever medium I have it installed on.
You may have to select which drive to boot from, but most systems auto-detect an OS install regardless of the OS.