My Date Just runs +- 3 seconds/day if I wear it constantly. If I switch out with another watch for a day the Rolex is usually way off. My Omega Seamaster coaxial is slow no matter what I do with it. I'm convinced that right out of the box any mid grade Japanese timepiece is equal to most Swiss products. I have an Orient Mako like the one getawheel has above and it runs and runs and doesn't care what I do to it.
One of the things with automatic watches is that most are regulated to assume they spend a good portion of the day fully wound and don't necessarily go more than ~12 hours without at least some winding. In theory, watches rate the same at the beginning and end of a wind(isochronic) but there are some subtle things that affect this also. In general, overcoils, which AFAIK every Rolex outside the Explorer has(for sure the Datejust does), improve isochronism but they're not perfect and can also introduce some weird properties when the amplitude drops below the designed value(as opposed to just uniformly speeding up like a simpler hairspring).
The Coaxial is certainly an interesting one, and Omega is on what, something like the 3rd or 4th generation now. I know at least one watchmaker who's been to Switzerland more than once for training on them-pretty much every time they updated their service procedure(no, don't oil the pallet jewels, okay do it, no wait only put a tiny amount on, no you're still using too much) and finally just refused to accept them since he says he can never get them to run as well as a lever even following what the factory trained him to do.
At least among American watch collectors, there can be some resentment toward the co-axial because George Daniels managed to talk his way out of a prior art claim on the patent despite the fact that it's basically a tweaked version of Fasoldt's escapement. There's a lot of split opinion as to whether Daniel's patent was really legitimate or not. Still, though, he managed to get it into mass production, whereas even though Fasoldt did sell some watch, his production numbers were in the hundreds at best.