On Windows you have a battle-tested Direct3D 9/11 backend for WebGL (ANGLE) used by Chrome and Firefox, while on other platforms you're subject to the whims of the GL implementation (and on Linux there are multiple drivers to choose from in some cases). Direct3D graphics are also thread-safe in a way that is not consistently true for OpenGL (just ask a driver developer) which means that certain operations could block the UI thread (or in the case of Chrome, GPU process) that can be performed asynchronously on Windows, resulting in a difference in application behavior.

On Windows there is one common software audio stack (they dropped hardware audio acceleration ages ago because it was a compatibility nightmare). On Linux in some circumstances there are multiple audio stacks which can produce differences in user experience and behavior. Recently Firefox has switched over to pulseaudio, which has caused some grief.

Windows and Mac and Linux all have different networking stacks that can result in behavioral differences between OSes if you're using WebSockets or WebRTC.

The GamePad API is also subject to OS differences depending on whether your gamepad has drivers and which underlying system API the browser uses. This even varies between browsers on the same machine.