The problem with Xanax and other benzos is that they can be very reinforcing if you use them too regularly. Even a very mild dependence can cause you to sweat more when off the drug, which will make you want to treat it, take more Xanax, just increasing the dependence, increasing the anxiety symptoms, including sweating, when off the drug, and you're probably smart enough to see how this can get one caught up in a vicious cycle.
I'm not saying not to try the Xanax. Used properly, a clonidine + low-dose xanax combination is probably going to be more pleasant than amitriptyline, although I still doubt it would be as effective. It's just important to be careful and not let your usage escalate and get out of hand.
I guess a real consideration to keep in mind would be how often you experience your sweating break-outs, and whether or not you can anticipate them. If it's not too frequently (2-3 times a week, max, in my opinion), and you can tell ahead of time that you're going to be sweating, clonidine and/or Xanax would probably be a more attractive option.
If it's happening on an almost daily basis, and you're really unable to tell when you're going to be sweating until you're already sweating, the amitriptyline would make more sense, in my opinion, as it's more suitable for 24/7 use. As effective as Xanax is for anxiety, you probably don't want to be on it too often (especially for something as benign as sweating) as it has the potential to just make things worse in the long run.