The MR as a day hike requires exactly the same permit as the main trail: DAY USE of Mt. Whitney Zone
But overnight use is outside the lottery -- you need the North Fork of Lone Pine Creek JM34
permit. Quota is 10 per day, 6 are reservable 6 months in advance, 4 are available to walk-ins at 11 AM the day before starting the hike.
The MR is shorter and steeper. But if you have to tramp through snow, shorter is better. The MR chute is only a little steeper than the Main Trail version. The Final 400 is definitely more technical than anything on the main trail -- steep third class. Guides rope-up their clients. Most without guides just go up. There is an alternate "Easy walk-off" route that is not as steep, but in May might have some nasty steep icy sections, so crampons and ice axe would be practically mandatory.
The other part of the MR: If you don't really know the route, you can get off track and waste lots of time thrashing around. Also, the Ebersbacher Ledges are legendary -- fun for many, terrifying for a few.
Here are the Mountaineers Route info and links
Find the link in the first post in the Reference forum.