Question

One using aerobic respiration and the other using anaerobic respiration - were competing for the same source of glucose in the same environment, which one would outcompete the other?

Answer 1

The anaerobic one would outcompete the other.

This is because anaerobic respiration occurs in the abscence of oxygen whereas aerobic respiration relies on the oxygen for survival.
If the environment has oxygen both anaerobic and aerobic respiration take place. But if, the environment lacks oxygen, anaerobic respiration takes place whereas aerobic respiration does not.

Hope it helped!