Noseband helps to keep a horse's head down as if they lift their head they can't see as well. Can be useful if you have a horse who doesn't like to be bitted up or doesn't like the action of a martingale.
Cheekpieces help to focus and channel a horse forwards, usually used on green or spooky horses.
oh thanks, so would the cheek pieces help my boy who doesn't like things coming up behind him. He seems ok until whatever it is gets level with him then he shoots forward.
No, I wouldn't use them for that purpose, its more for racehorses that need to concentrate on going forwards.
for your horse I would do some traffic training in a safe location with a friend driving (or riding a bike if it's bikes that are the problem). Also hacking out with a really traffic proof horse works well.