Just a quick video of me timing the two different paths at the end to see which is faster
0:00 test 1 time 11.50
0:40 test 2 time 11.46
1:16 test 3 time 11.31
If my timing is correct going to the right is 0.2 seconds faster but only if the door is open
You lose 0.4 seconds bashing through a door vs running through an open door