I am a software engineer. I have worked with Windows and Linux for years. To summarize this post: Pro Tools would probably run at least twice as fast on Linux as it does on Windows, if it were carefully ported.
Linux is a lot more efficient than Windows - that means more computation is possible for any given hardware configuration. How much more depends on many factors. Here is a
video that discusses benchmarks.
Microsoft provides Linux integration with Windows, called
WSL2. The default distribution is Ubuntu, with a kernel optimized by Microsoft. Microsoft is about to release a new graphical subsystem called
GWSL, which will allow Linux programs to display natively on Windows. Unfortunately, WSL2 runs as a virtual machine, which requires significant computational resources. This means that it would be undesirable to run Linux programs on WSL2 if native Windows versions are available.
Ubuntu recently switched to the
Wayland display manager, instead of the rusty old X11 display manager. This should help software vendors such as Avid provide video support for native Linux distros that support Wayland.