The global menu does have the aiming advantage. The sapce advantage is mixed. If you have windows side-by side (which seems more common than stacked vertically

The global menu does have the aiming advantage. The sapce advantage is mixed. If you have windows side-by side (which seems more common than stacked vertically) per-window is actually better as often the global menu doesn't take up the full width of the screen. Changing to the active window is actually a downside. It means that I need to activate a window before I can open the menu. Especially if the window is not at the top of the screen it can make a lot of travel distance to do those two clicks. There are definitely pros and cons to both options.