Neither will do anything to significantly reduce the amount of carbon we're pumping into the atmosphere.
1) Carbon taxation will either be dodged (employers will relocate overseas or to areas with lax regulatory environments, i.e. the American South), the cost passed onto the consumer, or will be ineffective entirely because other nations won't adopt the same tax because they'd see doing so as pointing them at a competitive disadvantage with the United States.
I think the point of a carbon tax is for it to be passed on to consumers. You want consumer to factor in the environmental cost of their behavior when they make decisions. You could also make a carbon tax revenue neutral by lowering other taxes, so I don't see how that's a major problem.
2) Cap and trade will create another economic bubble and will probably cause an economic collapse as speculators buy up pollution credits and sell them off in a haphazard fashion. This tends to happen when you create markets out of thin air (no pun intended), and this would have pretty terrible effects indeed. Also, there's no guarantee of American Capital complying with it, because we have to remember that they're willing to relocate and then ship goods back into the U.S. because those sort of activities are financially advantageous to them.
You can't relocate a power plant out of the United States. That's mostly what we're talking about. Most CO
2 emissions are energy production and transportation, not industrial. The things that are industrial mostly can't be off-shored, or they already would have been. There are things it still makes sense to produce in America, gasoline, cement, steel.
As for your theory, that's just a bold claim that you created out of thin air, no pun intended. We have plenty of other trading markets that work pretty well. Why is this one definitely going to lead to economic collapse?