It depends on several factors. As was mentioned hand held or on a tripod? I don't know if the hand held dampening theory put forth is accurate. The fact of the matter is the simple act of pressing the shutter release with your finger will impart plenty of vibrations on its own so whether the mirror is doing anything or not is immaterial.

You also have to factor in that the normal lens for most of the medium format cameras I've used is 80mm. With an APS-C DSLR you are looking at 30mm. Based purely on that alone you are going to have a considerably more blur prone experience with medium format. The other thing to consider is tripod. If you don't have a solid tripod in a lot of situations you will be wasting your time with mirror lock up. Your final print will only be as good as the weakest link in your work flow. My first tripod was one of those cheapy Vanguard plastic jobs you can get at Best Buy. Even with mirror lock up the results were often terrible. I eventually ponied up a whopping $80 and bought a used vintage Tiltall aluminum tripod in excellent condition. A bit too much bling for my taste but you can't argue with the results.

The other thing that matters somewhat is what camera you are using. I have been using a Rollei 6008 Integral lately. The camera has an electronic cable release that has two big buttons. One says mirror and the other says start. So to take a picture I press the mirror button and wait a few seconds then I press the start button and the picture is taken. The question is why wouldn't you use mirror lock up for every tripod shot. It really doesn't add any more effort. Now if you get some other camera system I've heard mirror lockup can be more cumbersome. In that situation you will have to decide for yourself.

This is an article about MLU from a 35mm SLR perspective. It's from 1998 but it is just as applicable today. The graph included is interesting.