The Mountaineers' Route involves some rock climbing while the main trail is, well, just a trail. However, the steepness of the MR means that one spends less time above 14,000 feet, less time exposed to the wind, and less time acting as a lightning rod. It's also shorter and, in my experience, a faster route. I'm planning my first attempt at a "double" next week. I'll use the MR for both trips up and at least the first trip down.
Changing the subject a little, I was on a four-day Williamson-Tyndall-Keith trip back in 1989. The do-do hit the fan just as we finished Tyndall. I got bored lying in my tent at the pothole, so I put on rain gear and headed for Keith. The storm weakened as I gained more elevation. I was probably more lucky than smart, but the fireworks were over by the time I got to 13,000 feet. I had beautiful weather on the summit, and made it back to camp just before dark.