Yes, a 390 (if in good shape) should wind up faster (take less time to get to a particular rpm) than a 360, especially under any load but, the cam timing and carburetion will also limit the rpm and time it takes to get to that rpm.
i.e. The 63, 352 2v was rated at 4300 rpm, while the 390 4v was rated at 4600 rpm. Different cams and carbs.