Aerobic respiration is a type of cellular respiration that occurs in the presence of oxygen. Anaerobic respiration occurs in the absence of oxygen. Both types of cellular respiration begin with glycolysis, the splitting of glucose.
Both aerobic respiration and anaerobic respiration need ATP for energy. Aerobic respiration gets its ATP from the Kreb's Cycle and Electron Transport Chain, processes that depend on the presence of oxygen. It also uses glycolysis.
What are the advantages of aerobic respiration?
Regular glycolysis, without the presence of oxygen, can only split glucose into two molecules of pyruvate, making just 2 ATP molecules. However, with oxygen, you can create up to 38 ATP molecules because more energy is produced.
In Anaerobic respiration, the ATP is procured exclusively by glycolysis; there is no oxygen to fuel either the Kreb's Cycle or Electron Transport Chain.
What are the advantages of anaerobic respiration?
The obvious benefit of anaerobic respiration is that organisms can survive in areas with little-no oxygen. E coli, for example, are anaerobic bacteria that live in the large intestines of humans.
Anaerobic respiration also occurs very quickly; it produces ATP fast. It gives your muscles short bursts of energy for intense activity (i.e 100m dash).
Resource: Here is a fun and informative rap by Tom McFadden, Stanford graduate, on the electron transport chain and Kreb's Cycle.