I think it completely depends on the horse. I ride in a bit and my horse is fine but I know my friend only rides in a hackmore and loves it. If you have a really strong horse a bit is typical but a bit less bridle is not out of the question because all horses can be trained to respond well to a hackmore. I personally like bits but bit less is also an awesome way to ride too. I think the decision is completely up to you!
I hope this helps!