I think the difference in handling a vocal like described (or any vocal for that matter) between those two mics is going to be more in high frequency transients than anything else. You will noticed that the RE 20 will have a more "muted" sound on transients above 2KHz compared to a LD condensor. That is about it though. If the singer is overly dynamic, well, they are overly dynamic. How the mic distorts from high SPL in close proximity WILL BE very different, but loud is loud, and quiet is quiet. The type of mic used in this case is not going to solve the problem.
Possibly, the RE 20 will give you a more consistent tonality on the voice if you back the singer away from it for louder passages. While this might help improve things a bit, you are now introducing more ambiance to the mic as the direct>indirect sound ratio has changed. You will hear more of the "room" when the singer backs away. This may or may not be acceptable for the problems it solves, but it is something that you need to consider.
Working with singers that are overly dynamic can be frustrating. It is really best that the singer is singing appropriate dynamically speaking to the music. But when that is not possible, you the engineer get the fun of trying to track that voice and keep somewhat of a consistent tonality on the track. One thing that you might try is to use a LD condensor set in an omni pattern. While this isn't as good as if the singer could just do what they need to do with a less dynamics, it may in fact prove to work out well in the end.
Good luck.
Oh, an RE 20 or 27n/d should be in EVERY studio mic pack!

What a great and versatile mic!
Ed