If not, have you considered why?
Recently, I have seen an influx of threads asking advice about "what bit to put my horse in because I don't have control of him/her?" As opposed to retyping my opinion several times, I just decided to have a bit of a 'rant' thread.
First off, if your horse simply refuses to listen to the bit, then the problem isn't with the bit. The problem lies with what training (or lack thereof) and handling the horse is getting. The fact is that 99% of the time that a horse is ignoring the bit, slinging his head, nosing out, or any other action that most people associate as a "bit problem", it isn't the bit at all. It is a terrible thing to see that so many people are not being taught how to properly cue a horse with the bit. They almost always have solid contact and in order to stop or turn, they just pull harder. Those people have hard hands. HARD HANDS MAKE HARD HORSES.
If the horse isn't as responsive as you like in the bit that you have, then work on him in the bit that you have. It is better to go back to a simple snaffle for schooling or corrective work though because it is one of the mildest bits that you can find. If a horse is responsive in a simple snaffle, then you can ride him in anything; however, if you ride him in a twisted wire gag for him to be responsive, then you would have no control in anything less. All the time we see it: a horse gets hard in the snaffle so they move him up to a twisted snaffle, then he gets hard in that so they move him up to a Tom Thumb bit (one of the most worthless bits ever made in my opinion), then he gets hard in that so they move him up to a solid mouth curb with longer shanks, then he gets hard in that so they move him up to a gag bit or a combination bit like those you see with a hard rope noseband and gag bit. Before you know it, the horse is being ridden in a 1/8 inch double twisted wire gag bit. Then 'what a miracle' the horse ends up hard to that too and at this point, they say "Well he is a stupid horse" or "He's stubborn" or "He gets excited". They never for one instant consider that every problem that horse has is rider error and by that point, the poor horse is usually beyond the point of no return.
Not many people are concerned with learning how to be soft with their hands and those that aren't will always blame the horse or the bit for every problem they have. You teach softness by being soft. You maintain softness by being soft. There are certain times, especially when handling a green horse, that being hard for an instant is required but it takes someone who understands horses and knows softness to know how much 'hard' is required and when it will be beneficial to the horse. Many riders should spend their lifetime riding with nothing more than a snaffle because they don't understand when, how, or why to use the bite that a curb bit has. Even fewer people have any business using a twisted wire bit for any reason. Those bits should be reserved for only the most experienced and talented horsemen to use on only the most outlaw horses and only for a few days to re-gain respect for the bit. They should never be used for everyday riding by your typical 'fun' rider, or even a competition rider.
Many horses that end up hard due to improper riding can be re-trained to be soft-ish, however, they will never be as soft as a horse that was taught from the beginning to be responsive to the slightest cues. If you are having trouble at the lope or gallop, then it isn't a sudden problem just because of the change of gait. The issues are there at the walk and trot, they are just more subtle. Any gaps in training at the slower gaits will reveal themselves at speed.
No horse that got the proper training or riding needs to be moved up from a snaffle. We, as riders, choose to move to a different bit because of our preferances or training goals. I choose to ride in a ported curb because I ride one handed on a loose rein and a ported curb is designed for that, a snaffle is not. However, I can still stick any of my horses in a snaffle bit and they respond the same way. If I rode all my horses on light contact and direct reined, would I still use the curb? Absolutely not because it isn't designed for that and it is too much bit for that type of riding. The more advanced bits are designed for finesse, not power.
Anyone who says their horse needs to be in this special bit is just kidding themselves. The horse needs that bit because his training and handling dictates that the rider needs that bit to communicate because their hands only know how to scream. They cannot understand the sublety of a whisper and as a result, their horse has learned to tune out all but the loudest of screams.
Are there horses out there that seem to be immune to the softness of the snaffle from day one? Of course, but those are very rare and that immunity is generally paired with an outlaw nature that is dangerous to handle anyway. If a horse can be trained to accept a rider, then they can be trained to be soft to a snaffle bit.
Some horses misbehave in the bit due to a physical issue, whether it is a tooth problem or a nerve problem in their mouth or some other reason that carrying a bit would be painful. Some riders simply choose to ride bitless. Does that make them less knowledgeable or have a lower worth as a horseman than someone who rides in a bit? No. However, the bitless options out there are no different than the bit options. There are very mild choices like a simple halter or sidepull, there are more advanced options like the bosal, and then there are ridiculous options like those chain nosed mechanical hackamores. The same rules apply to those as they do to bits; stick with the mildest choice unless you need more finesse as the training level progresses.
To make a long story short, a bigger bit is designed to create finesse later in training, they are not meant to simply give a rider more power. A power struggle with a horse will always end up with the horse ruined and the rider frustrated and hateful.
Results come from what you put in their head,
not what you put on it.