Open source apps often use less resources than proprietary apps, if that's what you mean. But running open source apps on windows or running proprietary apps on linux will not make a difference, proprietary apps use more resources and open source apps use less. If you mean as a whole then yes, running open source apps on linux will use fewer resources as a whole that open source apps on windows, but the only difference will be that windows itself will be taking more resources, not the apps.