Windows and macOS computers becoming slow or unstable after updates - what should I check first

I've noticed that both Windows PCs and Macs can sometimes become slower after system updates. Some users experience longer startup times, applications freezing, or unexpected software issues.

What troubleshooting steps would you recommend checking first before considering a system reset or reinstalling the operating system?

Would you start with background processes, available storage, startup applications, or checking for driver and software compatibility issues?

I'd be interested to hear how others approach these problems on both Windows and macOS.