Archer's ship is as large as Kirk's
No, it isn't.
The NX class is 225 meters long, 135.8 meters wide, 33.3 meters high.
class is 289 meters long. We don't know its width, but we do know its height is also greater than an NX, due to the secondary hull.
Also, the mass of the NX is much less. The NX is about 80,000 tons in mass; the Connie is almost a million.