Here's a statue and a carving of Akhenaten, here’s one of Ramses the second. While Ramses's depiction is standard for how the pharoah's generally were depicted, Akhenaten looks almost alien-like with his slanted eyes, elongated head, slender frame and wide hips. What is the reasoning behind this depiction? I know that there was sort of a character-assassination policy led by his son Tutankhamun to tarnish his legacy (which is what I assumed was the reasoning behind this bizarre depiction, as sort of an insulting reminder of the heretic that almost destroyed the Egyptian religion), but most of the statues/carvings depicting him were made when he was alive, with his permission and blessing. Did he have some kind of ailment or disease like his son (who was still shown to be normal looking in his statues and carvings) from successive generations of inbreeding? or was he a foreigner who looked different from the rest of the population?
Akhenaten was revolutionary in many ways and it is completely reasonable to assume that Amarna Egypt also rewarded revolutionary changes in art.
Several things are going on there: Akhenaten not only was overthrowing the artistic world, he was also overthrowing dominant religion of ancient Egypt and in fact moving his entire capital to a new, purpose-built city. He is thought to be one of the first monotheists, which is an interesting but ultimately irrelevant point — there are current theories that his overthrow of the worship of Egypt's many deities, most particularly the dominant cult of Amun, was not terribly different from Henry VIII's plundering the monasteries of England in the Tudor period. The religious establishment had wealth, which equalled power, which equalled influence, which equalled a threat to an iconoclastic monarch.
It is hard to conclusively establish why Amarna art was so different — theories about wicked royal inbreeding, usually Marfan syndrome, are not unusual but mummies from that period show problems but not the speculated genetic disorders that would lead to Akhenaten appearing terribly different. We do not know which mummy is definitely Akhenaten, but current speculation is on the mummy found in KV55.
But when you commission an entire city which is promptly deserted after your reign, you have a lot more influence over the aesthetics on display than you do with a normal city that has temples and figurative art and displays that were done over generations.
As any modern commercial artist could tell you, you present sketches to the client and work with their criticism regardless of what you think. It is very likely that Akhenaten developed a particular aesthetic that he rewarded with more commissions to artists that favored his artistic style.
If you are very interested in New Kingdom art history, then you will be interested in Aidan Dodson's Amarna Sunset and Amarna Sunrise. One of the most accessible scholarly articles is Martha Bell's "An Armchair Excavation of KV55" discussing KV55. You may find interesting information in this question in /r/AskHistorians by the great /u/tweedy_impertinence (nice Wire shout-out) on Amarna art.