If you are doing big shows, like Classics, or Medals - then I'd say Button Braid.
Majority don't even braid for most Jumper shows, you rarely see braids unless it is GP or Medals or the Classic.
There is no "In" or "out" in Jumpers - it is primarily about competition, period. Not whether the horse has Button Braids, Hunter Braids or a Running Braid. Most don't care whether you have a braided mane or not, it is about performance - and who cares what others think? Just leave the rails up and show them how to get it done :)
If you do a Running Braid, make sure it is clean, tidy and neat.
I personally - don't braid at all. I prefer to have mane to wrap my fingers around over fences, can't do that with braids.