Whether or not oxygen is in the tank isn't a minor process detail. It determines which microorganisms show up, what they excrete, how fast they work, and whether the process costs energy or makes some back.
Aerobic digestion uses microorganisms that require oxygen to metabolize organic waste — which means the process requires actively supplying oxygen, usually by mechanically aerating the tank. Anaerobic digestionuses an entirely different community of microorganisms that function specifically in the absence of oxygen — oxygen is actually toxic to some of the key species involved — inside a sealed, oxygen-excluded tank. Same general goal (breaking down organic waste), two biologically incompatible ways of getting there, with different byproducts, different speeds, and — critically — opposite effects on the treatment plant's energy budget.