I've used all of these 'gadgets' at different points, I can give you a quick lowdown on how I've
personally used them, but everyone does have different opinions and at the end of the day it depends what your horse needs!
Firstly, my fave bit of this kit is most definitely side reins. I use these on all my youngsters when lunging (after a period of fitness work) to encourage the horse to accept a contact and start to work in a frame. The trick is to keep them loose, they don't pin the head in but instead they don't allow the horse to stick it's nose out, and the horse has to carry itself when they give to the contact. Don't use the ones with elastic insets though, as that can teach a horse to lean on the contact.
However, the downside to side reins is that they're not adjustable in a split second, and have no give. For horses with very sensitive mouths, or who have a tendency to throw their heads around, or sometimes just with youngsters who are unsure of what is happening and can be reactive, they can actually cause a horse to rear (especially if too tight). So before I introduce side reins (and I do it very slowly, one loose rein at a time first and gradually tightening over a week or so and introducing the second rein) I sometimes use a home-made device I call a 'bungee' instead, and for some horses as a complete replacement.
My 'bungee' is a length of bungee cord with a clip at either end. The middle of the cord sits on the headpiece, with either end of cord going through the rings of the snaffle, and then clipping to a piece of felt I look around the girth, between the legs. This is probably an actual gadget of some sort, but I just made my own as I like it better than the chambon. I like it because it is completely flexible, and if the horse panics and pulls its head up there is resistance, but its not inflexible. (Kind of like an elasticated de gogue, I guess, with more give and only for lunging)
A chambon I've only used with horses who really fight the bungee and lean on it, but are too green or too flighty and I don't trust with side reins. This way, there is pressure on the mouth but not the poll the way there is with a bungee, and horses can't learn to lean on it the same way. But I don't like them for horses who I can work in side reins or a bungee, as the fact that the chambon doesn't have a downwards pressure, only a pressure on the mouth that increases as the head rises, can encourage rearing. They can also be useful for horses that have really learnt to dip their backs away from a rider's weight, though...
Basically, it depends on the horse. All of these are only for lunging in in my opinion though, as there is no way of releasing the pressure when mounted, and you don't want to be mounted if a horse does decide to flip. However, I would always lunge in one or other of these gadgets, depending on the horse - I would ride my horse in some sort of contact when schooling, so I think some way of asking for contact while lunging encourages a horse to work better. Ideal world, side reins, for me.
The draw reins though I consider much more gadgety. Once you've started riding a horse, if they've been properly started they shouldn't need gadgets to pin their head in - they've learnt from the side reins how to give when the contact is apple,d and how to carry themselves, so shouldn't need it. But, for fixing up horses who have been taught to brace against a contact and hollow out their backs, draw reins can be useful - it allows a horse who has difficulty bringing the back up to lean on the contact a little to balance before bringing the back up. Not ideal, I know, so I don't tend to use them often, but if it's going to be my back or draw reins that they brace on for that first period of building up new muscles, I'd rather it was draw reins. From there, I'd go to a market harborough and as soon as the horse has learned to give properly when contact is applied, to nothing. Draw reins are SO EASY TO USE WRONGLY though, as they tighten up very easily and can end up pinning a horse's head down to a degree where it can really hurt them. Far worse for them than even hauling on the bit all the time. So use with caution.
Bit of an essay, but essentially: side reins, good; bungee, good; chambon, third choice, but useful; draw reins, if your horse is really messed up with regards to reaction to contact, they can be useful, but use with caution.