The Nitrogen Cycle is probably the most important invisible process that goes on within the confines of the aquarium. In essence it is nature's answer to the simple fact that fish and other oganisms produce toxins in the environment that can easily build to concentrations that are high enough to kill. Other sources are from the natural decay processes produced by bacteria acting on dead organic material such as excess food, dead leaves, dead fish and the fluctuating populations of invisible bacteria as well. The bacteria form colonies wherever their needs are satisfied, they must have an adequate supply of oxygen passing as well as the ammonia that is their energy source.
Ammonia is extremely toxic.
It is deadly in relatively small concentrations in the aquarium. Between the two methods, I personally prefer the biological removal by promoting nitrosomonas populations. The biological bed will adjust to environmental changes over time and is the best defense against stress on the fish that I know about. Roughly double concentrations of nitrite can be tolerated before death occurs. Nevertheless, the whole idea is to understand the role of both toxins to control them and keep your fish alive.