The Justice League Snyder Cut restored Snyder's vision for the superhero film three and a half years after the reconfigured theatrical cut was released with all of its infamous reshoots. With the Snyder Cut finally out as the intended next DC movie after Wonder Woman, it has more direct connective tissue for David Thewlis’ God of War, Ares.
Ares was the main villain in Wonder Woman, disguising himself among humans as Sir Patrick Morgan. Thewlis’ appearance in Wonder Woman largely shows him in completely human form and he also doesn’t utilize his powers until the final fight with Diana, instead acting as a nefarious voice from the shadows nudging humans to decisions that provoke them to war. Though he was still a tough enemy for Diana (Gal Gadot) to take down, Ares' victory over Darkseid in the Snyder Cut indicates his power had been lessened after later being cast from Mount Olympus by Zeus.
In the Snyder Cut, Ares makes a brief appearance in the history lesson, with Thewlis’ face added onto the body of stunt man Nick McKinless. The ancient battle, in which the armies of man, the Olympian gods, and the Green Lantern Yalan Gur repel the invasion of Darkseid (Ray Porter), sets the gods apart by depicting them as roughly eight or so feet tall. Ares strikes down Darkseid, not yet in possession of the Omega Sanction, with a single chop of his axe, and these elements recontextualize his Wonder Woman role in of his portrayed power. His clearly diminished physical prowess ahead of the final battle against Diana could indicate that, having left Olympus, his power is not as potent as it once was, explaining his comparative weakness in Wonder Woman.
Of course, even a not-fully powered Ares as one of the Old Gods would still face a dangerous opponent in Diana, revealed to be Zeus’ designated god-killer by Ares in Wonder Woman’s finale. Nonetheless, Ares’ largely clandestine activities over the centuries of quietly guiding humanity to destroy itself show his partial de-powering forced him to operate behind the scenes more. Ares’ height difference from Wonder Woman to Zack Snyder’s Justice League also is a subtle hint that Ares was once a more powerful demi-god.
By having the contrast of Ares in the two films, Jenkins and Snyder portray Ares at two different stages in his life. In the Snyder Cut's history lesson, Snyder shows Ares in his full God of War form, complete with his great height and defeat of Darkseid with one strike. In Wonder Woman, Jenkins shows Ares in his “fallen” form and more typical human height, with his powers having been weakened, though still strong enough to hold his own against Wonder Woman (originally in the Crimean War.) Ares' shortened height is a visual signal of his fall and somewhat lesser strength. While Ares does seem bigger fighting Diana when he dons his armor, he might have simply added makeshift lifts in his boots, with his armor suit being crudely constructed fast via telekinesis.
The history lesson in Justice League’s theatrical cut was greatly truncated and shifted around with editing and didn’t afford audiences the intended look at the Olympian gods. With the Snyder Cut’s version of the history lesson, it not only did that, but added stronger links with Wonder Woman. Both it and Zack Snyder’s Justice League show Ares at two different power levels, though still extremely strong, but the latter showing Ares in his prime and full Olympian height in the battle with Darkseid for the Anti-Life Equation.