I think it makes more sense to put the cost on the emissions themselves (i.e. their production), not on the end-products. In a perfect world these two approaches would be equivalent, but since there are relatively few emission sources compared to end products, I think it would be easier to enforce.

The problem with mixing carbon taxes with global trade in general is that if some countries don't participate in carbon taxation, then carbon-intensive production will just shift to those countries. Game-theoretically, it's a relatively unstable equilibrium because if all countries are participating, then a country that suddenly refuses carbon taxation could stand to benefit enormously.