Hello
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I like them both in the right hands, but preferr the german martingale because it does absolutely nothing when the horse's head is in the correct position. It only checks the horse when his head moves into the wrong spot, giving him release when he corrects himself.
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With the draw reins, you can just keep pulling and pulling until the horse's chin is on his chest and you can still keep pulling - thus giving the horse no release (that's when its used in bad hands though). In good hands, the draw reins can be very effective for suppling exercises and achieving good head position. But its easier to make a mistake with these as opposed to the German Martingale I think...
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I use both of these with great care on very rare occasions to help with my training. But I find that these items are no substitute for good hands.
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I also noticed your posting about the horse's teeth. If you are looking at using these tools on that horse, make sure her teeth are done first by a professional and give her a chance in the bit you normally use once she has recovered from the dental work before you try these out just to see if there is any improvement. You may be pleasantly surprised :-)
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It can be nothing short of incredible the difference having the teeth done can make in a horse's behaviour and response to the bit.
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It takes about two or three days for the horse's mouth to recover from the dental work sometimes. The Dentist will advise you on this though.
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Good luck, and I hope it all works out well for you :-)
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Kind regards,
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Gen

Thank u for the help. She good about her head most the time keep it pretty low and carry her self good but when she dose not want to do something ahe throw her head in the air to avoid my hands. And the past couple ride she has been really back but only when it come to her backing or doing something new that she dose not want to do. I was just looking at her teeth and saw she has a new one coming in. So I guessing that some of it and I have had her teeth checked he said there was nothing he could notice he could of missed something. It was not my normal guy who look at her teeth. So ill have then look at again. I just went out there to feed them and felt her teeth and she has no Sharp point and there smooth. But thank u ill have them look at again. Is it normal for a 6 year old to still be getting teeth??

Hello again :-)
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I'm not sure about how old horses are when they stop getting new teeth, but I do know that their teeth need to be done (floated) by a professional Equine Dentist at least once every 12 months to keep them in good shape.
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They should have their teeth done for the first time prior to starting and mouthing.
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Not sure what you could do about the head tossing, that's not something I have ever had to deal with myself, but I think the German Martingale would be a better tool for this than the Draw Reins...
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Hopefully someone with more experience than me will hop on and give you their thoughts on how to deal with the head tossing. The bit you are using could be too harsh for her perhaps; or it could be a "willingness" issue - could be a lot of things :-/
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Good luck with your mare :-)
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See you later,
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Gen

Thank u so much.. I'm going to have her teeth looked at. Thank u again!!!:-)