Basically the same uniform, but with metal patches and a different collar, since its closer to The Cage than TOS.
The Constitution will look basically the same (different in detail for higher resolution screens), but it seems logical to leave the basic shape alone for this series. Especially given how the rest of he fleet looks. A traditional Constitution-class vessel will stand out in that sort of fleet, and that is sort of what you want it to do. Stand out as something special and trigger that nostalgia factor, be it the Enterprise or not.
Given the trends, they would likely add self illumination to the ship.
The Constitution will look basically the same (different in detail for higher resolution screens), but it seems logical to leave the basic shape alone for this series. Especially given how the rest of he fleet looks. A traditional Constitution-class vessel will stand out in that sort of fleet, and that is sort of what you want it to do. Stand out as something special and trigger that nostalgia factor, be it the Enterprise or not.
Given the trends, they would likely add self illumination to the ship.