I was reading a report somewhere where it was said that Carl Hester said use a flash on a horse who you want to take the contact forward and use a drop on a horse who is quite strong in the contact.
I decided to experiment with my horse who has been in a drop for a while and move back to the flash as he has been difficult in the contact and actually he has been stronger in the contact since moving to the flash though I would say he is slightly more wooden through the jaw.
Its not a miracle answer but certainly gives food for thought and it was interesting for me to hear a top dressage rider differentiate between the two nosebands.
I posted that on HHO. I have done the opposite and moved from Flash to Drop and it has really helped soften and lighten her in the canter.
I too was really interested in the differentiation as I had never heard it described like that before.