The Cyrodiilic Akatosh is based on the Altmeri Auriel, a genocidal warrior king who wants to see all Men wiped out and Mer to be freeded from Mundus.
Except the Nords didn't like the Elven pantheon too much back then, so they threatened to abandon Alessia's... "Empire". So Alessia made Akatosh a lot more Man friendly, pro-Mundus, and all together more Shezarr like.
I'm not seeing that many parallels between Auriel and Akatosh, even if in-universe they're considered the same being. Akatosh seems closer to the Dragons' god than the Elves god, while Auriel is ironically more like Alduin. The thing is, we don't know much about Borhamu or what the dragons think of him, considering his creations followed Alduin, who posed as the him. And there's a much stronger connection with the Dragon God because of Akatosh's strong association with the Dragonborn.
Ever since Alessia, the Dragon God was linked to the Dragonborn, as he also appeared to Tiber Septim/Hjalti in a vision at Sancre Tor and appeared through Martin's sacrifice. And it seems the Dragonborn possess the same need to dominate as the Dragons, hence both Reman's and Tiber Septim's conquests (especially if we take MK's latest work under the name Eyesore to be canon), and Tiber Septim's questionable peacetime use of Numidium. Yet through the Dragonborn, the undoing of the world, which is what Auriel and Alduin seek, has been thwarted repeatedly.
Personally, I find it interesting that Paarthurnax uses the name Akatosh at all, considering he spends most of his time at the Throat of the World.
Edit: Fixed some wording.