The Day Date AT is indeed a bit less than a mm thicker than the small seconds. Neither is ungainly thick, I don’t think.
No doubt Rolex is the king when it comes to an iconic Day Date watch, and it’s inconceivable that Omega didn’t have that design in mind when creating the AT with its vaulted day display at the top. Still, within the narrow “orchard” of DD watches—apples and oranges here. The classic Rolex design is totally gorgeous but much dressier, only made in precious metal, and—in its classical proportions—smaller, at 36mm. (The larger ones are far less attractive, I think.) Amazing watches (I had the pleasure of owning one for a short time), but a totally different niche and price point. The AT one is sportier—available on rubber, even, larger, steel (at least most variants are), and far less expensive. Not the same vibe.
I dare say, owning one of each of those Day Dates would be a damn fine two-watch collection!