Generally, you want some sort of control over what happens when the user presses Stop. Using the Stop or Quit LabView functions abort anything LabView's doing (more or less instantly). The more complicated your program, the more likely you want a controlled stop to get to a known state. Saving results, closing files, shutting down power to Unit Under Test are part of a long list of things you might want to do before stopping.
So you may need to use local variables for a Stop button checked in multiple locations. If you have sub-VIs running which run loops, you may need to use a global rather than a local to check Stop in the sub-VIs.
You may not need to check Stop in as many locations as you think. Start with the long running loops and sub-VIs and see if your
Stop is fast enough without checking Stop everywhere.