The "false grip" is what determines whether the muscle-up is an exercise worth doing, or if it's just a gym trick with little actual training benefits.
Use the false grip and you'll be able to "peak" your body by applying muscular force to the bar or rings. Don’t use it and you'll need to peak your body by relying on swinging and momentum to get above the bar.
With the false grip (flexed wrists, palms on top of the bar) you're able to dip out of the transition from pull-up to dip. With the pull-up grip (wrists neutral, palms in front of the bar), you'll have to use momentum.
There's a vicious rumor being spread by unknown parties that you should probably know about. Now, this rumor is pretty ugly so be prepared. Are you ready?
Unfortunately, your old "what do ya wanna work today?" spur of the moment type training works a whole lot better than anything the Soviet Ministry Of Sport managed to cook up behind the Iron Curtain back in the 50's and 60's. Charles Staley explains why.