A drop noseband is literally designed to stabilize the bit, it’s why it’s the go to nose noseband for green horses in Europe. It’s a shame it’s gone out of style here.
the flash is designed to limit mouth movement and can therefore result in a more stable mouth feel.
the question is, is the horse fussy because he wants less bit movement? If so, use a drop.
is he fussy because he likes to play/ picked up a habit from past bits? Then a flash can help
or, is he fussy because he needs a different bit?
or because he needs to be more in front of the leg?