Whether you're playing on the PS4 Pro, Xbox One X, or a souped up PC, Assassin's Creed: Odyssey has some wonderful technical touches regardless.
A breakdown of Odyssey's engine from Digital Foundry shows that most of the visuals, including the nice screen space reflections on water, god rays, and depth of field in cutscenes, are shared between the two consoles. There's even nice touches, like Ikaros casting a shadow from far, far away.
Odyssey uses dynamic resolution — as do most games in the current generation — and as you'd expect due to the hardware differential, the Xbox One X has a resolution advantage at differing points. At heavier loads, particularly the first fight of the game which has scores of NPCs battling away, the PS4 Pro dipped to a low of 1242p. The Xbox One X, meanwhile, hovered at 1656p.
A major difference between the two consoles is the increased draw distance and improved streaming on the Xbox One X, with some nicer ambient occlusion on the Microsoft machine. Both consoles use largely the same assets, however, so it takes a lot of freeze framing to isolate the differences.
Performance is similar on both consoles: a locked 30fps experience that drops occasionally, potentially because of the CPU limitations in both consoles. The main kicker is some slight 1fps hitching when the camera pans.
But while the Xbox One X has a natural edge, the experience isn't materially different on either enhanced console. It's much the same situation we saw with Origins, which isn't a surprise given much of the base tech has carried over. Odyssey makes some small improvements here and there, but by and large Odyssey holds its own just fine regardless of the platform.