Okay, I'll chime into the debate going on with Chiilla and Muppet.
I bit up when I go to shows. Why? Because horses get strong at shows. Otherwise, I would be in a snaffle til the day I died or the horses finally succeeded in paralyzing me.
Some horses do fine at home. All of mine do. They are comfortable
there. Things often can't be fixed at home. That's why we "season" our horses to show. If everything was fixable at home, such as bit responsiveness, we'd all be able to work at home and then come steal each other's money at shows without seasoning.
I agree, sometimes it is a training problem. Other times, the horse is just excited to be in a new place. Horses are capable of learning how to take advantage of a particular bit. Some flat out just learn how to lean on a snaffle because of the rider's hands. They learn the action and they know how long they ahve before the hammer comes down on their face. This is why I switch bits often. Snaffle to jr. Cowhorse to a short shank Myler to a long shank Pozzi, then to a combo and back to a snaffle and then finally whatever bit they need to run or show in. The horses don't have time to learn to lean on a bit because they don't know what's coming. I am fortunate that both horses I have now are not the type to lean or test me, therefore they are always in a snaffle to train and then an actual show bit.
Now, this method is not for everyone. You have to be a horseman and know what is going to help your horse out.
Also I always hear about horses learning to lean on a strong bit after bitting up (and I have repeated and preached about it myself) yet I have legitimately never seen it happen, and I've been at a training barn and been showing my entire life. I'm going to ask my own trainer if she's seen it either, because I'm interested now. I remember someone else saying they hadn't seen it either. I wonder.