It would be an overgeneralisation to say one was better than the other. The OS is accessing the disk because it's being asked to. The question is: what is asking to access the disk and why? If the disk contains parts of the OS or system components such as swap files, then it's going to get spun up whether you like it or not.
Windows has typically included more background services and applications 'out of the box' (Whether these are wanted or unwanted depends on your point of view). So many peoples perception is that Windows is worse in this respect and they are probably correct. However, Microsoft have been paring back the basic installation for some years, especially in the server versions of the OS (the desktop versions are being integrated with Microsoft cloud services and have gone the opposite way in some respects), so the situation has improved, at least for servers.
Ultimately, Linux is much more configurable than Windows, so it should be possible to build a 'cleaner' system with it. It would be interesting to compare a minimal installation of a Linux server distro with Windows Nano Server in this respect.