Go with the hack. If its what he works best in, thats what you should go with. No one should judge you on riding a hack...I know lots of gamers who will only ride hacks and their horses are well trained. Some horses just don't like bits.
If it is like an obstacle challenge, you wont be judged so much on your tack as you will be judged on the way your horse handles obstacles. To give him the best chance to succeed, go with what makes him the most comfortable. The girl who won a local Obstacle Challenge this year rode in mismatched tack, blue jeans and a button up short sleeved shirt. Her horse did great though!