Standing in front of LVBS:
Exited from The Tops or the Ultra-Luxe. 1 transition.
Enter the LVBS or fast travel to the outside of McCarran. 2 transitions total.
Take the monorail to McCarran or enter the tent city portion of McCarran. 3 transitions total.
Enter the McCarran terminal building from the exterior monorail drop point or enter through the main doors. 4 transitions total.
Proceed to the concourse/exterior base (obstacle course, behind the terminal building). 5 transitions total.
Enter the supply shack. 6 transitions total.
The transitions are identical (if needing to visit the tent city area then fast travel wins), if you change the scenario to be anywhere except inside or right outside the LVBS, fast travel gains the advantage. This same principle holds true for McCarran, the monorail only gains the advantage if the player is inside the terminal building or concourse (since it has no direct route outside).
Standing in the supply shack:
Exit into the open. 1 transition.
Fast travel to the north gate or enter the terminal building. 2 transitions.
Enter the strip or enter the monorail platform. 3 transitions.
Enter the second section of the strip or take the monorail to the LVBS. 4 transitions.
Exit the LVBS. 5 transitions. (3 transitions versus 4 if both paths begins in the tent city or aircraft storage area)
Standing in the Concourse:
Exit the concourse into the terminal building. 1 transition.
Exit onto the monorail platform. 2 transitions.
Fast travel to the north gate or take the monorail. 3 transitions.
Exit the LVBS or enter the first section of the strip. 4 transitions.
Enter the second section of the strip. 5 transitions. (3 transitions versus 4 if both paths begin in the terminal building)
The most obvious method of making the monorail effective would be to make the New Vegas end let out at the exterior of the LVBS (with access to the strip immediately) and the McCarran end of the line actually let out directly into the McCarran terminal building (without having to enter from outside). I don't know how difficult that would be, though if it can be accomplished then the monorail would actually be more efficient or identical to fast travel regardless of which section the player was in on the Strip or inside McCarran.