aerobic decomposition leads to a balanced feed that most importantly seeds a plethora of beneficial bacteria. it is often monitored by temperature with a thermometer and in commercial situations, especially when it is transformed to compost tea, it is monitored by a microscope. here is an article i wrote on hot compost
https://treeyopermacultureedu.wordpress.com/chapter-8-soils/thermophilic-composting-hot/
Anaerobic conditions inside of hot compost piles produce phenols, alcohols and other nasty organic chemistry not so good for plants. however there are types of anaerobic breakdown that are beneficial for life. this is mainly down with lactobacillus and alters rather than a rotting process that does produce strong smells. this is why bokashi has long been used in the orient and i use sauerkraut juice in my garden. lactobacillus are great for gardens especially brassicas.
all people have their styles with composting, like food choices its very personal. this is what i have practiced and come to understand after many years of trial and error and studying and working with Dr Ingham.