Yeah, it's a "simpler" way to use draw reins but I can't say I'm overly crazy about them. Everyone seems to be using them as this big fad to get a horse "in frame" and because they're harder to screw up then draw reins, it's unbelieveable the number of novices using them. What irritates me is I always see them cranked to the max and people jumping with them - it's so unneccesary. I'm an advocate of properly used draw reins as an encouragement tool but a German martingale basically makes it so you can "strap" a horse into place. Again, properly used I'm sure they have their benefits but I've seen them so misused it's hard not to be cynical.
The second picture is a perfect example - they're clipped as high as they can go, and on a loose rein they appear alright, but if you just imagine a person collecting those reins English style, you can see how his nose would be literally FORCED to his chest if someone had an unrelenting contact. Hence why I prefer draw reins, you can select your exact desired amount of contact and resistance and can use them for encouragement rather then force.
If used correctly it is a fantastic piece of equipment - a lot less open to abuse than draw or running reins as they can only be adjusted so much and despite what some may think a horse can actually learn from wearing one - I use one to great effect with no ill effects for my horse ( or horses ) and I've been using them for 20 years.
Like many saddlery items they are mis-used and mis-understood, after all a wet paper bag can be a bad thing in the wrong hands.
It's an AID and if I had to throw out everything in the barn but one I'd keep the German Martingale. It slows the action of the hands to the bit and keeps a heavy handed rider from ripping on the mouth. You still have lateral control unlike some of the draw rein configurations. It's fairly mild but effective in maintaining head control. Most people would benefit by throwing away the draw reins, running martingales, nose bands, etc. and using the German Martingale as an AID. If you don't know how to drive your horse forward and balance the horse all the aids in the world won't help.
Sorry, not much help here, as I generally don't use any kind of 'aid' to help a horse learn how to drop his head, or develop a proper frame under saddle.
On the ground, I will use a syrcingle and draw reins for longe work, but they are always connected to the side, not underneath like that one is designed to. They certainly aren't 'cranked' tight either.
I've used one, it was a reinforcement tool for my mare as she became closer to being finished, I wasn't the only one who rode her in it either, she would get that you can't make me attitude with others that she wouldn't have with me so it helped her realize that she is supposed to work in the same frame despite the rider not being me. She always had a good mouth and an engaged hind end but she just liked to be lazy and kinda poke her nose out unless the drill seargent (me) was on her. She still has a good mouth and doesn't require it anymore so I think it did its job.