I'm not sure what you mean by "not common" the words are not synonyms and asphyxiation is used quite often. Choking has it's most common use in choking on food, it specifically means the blocking of the throat/air way and isn't really applicable for the common uses on this website. Asphyxiation on the other hand means oxygen deprivation which can be done in various ways.

asphyxiation is way more broad than choking, it includes drowning and other forms of oxygen loss