The second is a wonder bit or a beval bit, whichever name suits you. You are going to get less leverage with that bit then a regular gag with rope or leather cheeks. The wonder gag has a smaller range of motion. It only works to a certin extent, when the mouthpiece hits the top ring, then it stays on max power, which is not as intense as max power on a regular gag, until the horse or the rider releases.
I would start there when starting to use a gag. Then if that doesn't work, the regular gag with leather cheeks and if you still need a quicker response then the regular gag with rope cheeks. Make sure to have two reins on the regular gag. One on the snaffle and one on the cheek piece.
I am on my phone 90% of the time. Please ignore typos, misplaced lower case letters, and the random word butchered by autocowreck.
From my training many, many years ago and from ongoing experience since: a cheltenham gag (the traditional kind with rope or leather running through the bit rings) is a mechanical bit which helps to RAISE the horse's head. I have found it expecially useful and effective on horses who gallop with their heads low, leaning on the rider or those who gallop with their necks out in front with noses stuck out (if you can picture that).
On the other hand the beval bit is good for a horse which either sticks its nose straight out in front of it, or raises its head - the bit does seem to help to encourage the horse to drop his head and almost "come into a frame".
Links in the middle tend to also encourage a horse to drop its head onto the bit, to take a contact.
Every horse is different though and other people will have completely opposing views - so in the end, you will have to try both bits and see which one works best for you.
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I'd like something like the bit you use on Jake (this one), but it needs to be a five inch (He made it VERY clear he won't accept bigger bits). I'd be okay with trying a french link gag, or preferable a french link with a bean instead of the flat piece, but I can't find very many options in the regular gag, but I'm finding quite a few in the beval gag. HS makes one, but I can't justify spending $150 on a bit without trying it first.
If you don't mind a flat french link, if you know a shop that carries Jack's Manufacturing, they have a 5" french link eggbutt gag. I got a 5.5" from them and my horse goes very well in it (he fits the "gallop with his head low" model).
PM me if you don't have any luck.
I did not have much luck with my horse in the beval bit, it works more like a mild two/three ring than a traditional gag bit.
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