It all depends upon the camera that you own and how well the mirror is dampened.
For years Pentax 645 and 645n camera owners begged for a mirror lock up. Pentax claimed that it was not necessary because their mirror was so well dampened. Pentax finally relented and produced the Nll with MLU. Tests were run and the results were that the MLU made absolutely no difference. I have owned all three cameras and I couldn't see a difference.
I also saw a test where a Rollieflex, Mamiya RZ67, Hasselblad 500cm and another camera were tested hand held for vibration. Of course the Rollieflex (without mirror) came in first. Surprisingly the heavy RZ with larger mirror came in second and the light Hasselblad came in last.
In my opinion, if you want the sharpest image then shoot with your camera mounted on a good tripod with cable release and use mirror lockup.