I can vouch from experience that a well fitting bridle makes a world of difference. I started riding my horse with a western bridle and bit that were too small for him. I finally got an english bridle that fit perfectly and his behaviour improved dramatically and instantaneously!
It's ironic i saw this today, because yesterday me and my mom decided to start looking for and english bridle for the horse i am leasing(i ride her english but she's ridden in a western bridle)and this really helps! i can say it does help to have a bridle that fits correctly because yesterday i found out the western bridle wasn't adjusted the way it should have been.