I thought my reply was properly qualified by stating that the two projectiles had to be launched at the same angle. Obviously point of impact changes, but this is due to the barrel harmonics previously mentioned. If your barrel weebles instead of wobbling at the instant of projectile exit, then you will not have identical launching angles.
I think maybe I thought too hard on this one and gave the physics answer, when others were thinking of the practical application, which is of course that the rifle has to be re-sighted in. However, once that rifle is sighted in with the new load with the same projectile and velocity, the trajectory will be the same. For example, if you were previously sighted in dead on at 200 yards and were 2 inches high at 100 and 8 inches low at 300, then once you sight in your new load of identical velocity for 200 yards, the other figures will still apply. I apologize for any confusion.