the mecate line still attaches to the bit, so if you tie the horse with it, you are still tying a horse via his mouth.
They are handy if you need to lead your horse down a trail or place where you may need to send your horse ahead of you, like over a ditch or creek, and you need more line. And, like you mentioned, if you need to do a quick lunge session for obedience. But, the mecate only attaches to one side of the bridle, so there are thingsyou might have to do to be able to lunge from each side.
If the mecate is too long, it gets in the way. the one I bought is 22 ' and it's too long. It is often getting in my way.
you are supposed to wear a belt and tuck a fold of the mecate line into your belt, in a way that it will not tighten if you should fall off, but will stay in your belt as you ride . this allows you to access it quickly for "reminder" pops to the horse , if necessaery, and as a lead the minute you step off the horse.
As for the one you have selected, the only real difference is the diameter of the rope; whether she will like a half inch or larger (5/8) some folks find rope reins hard to get used to as it is. I think I might prefer the half inch to the 5/8, but the dif is small.