The size of the carbon tax has to be set by the government. Do we want to be taxed? No. Do we want to be capped? No. Do we want everyone to do something about climate change? Yes.
Then, when you come to the actual details of it, a little switch here or there changes everything so much. People say cap and trade. Okay, but if the base year is 2010, we're not happy. If the base year is 1990, cap away. The actual details matter so much that it is hard to judge. It's like asking whether we think screwdrivers or hammers are better instruments. It depends where and for what.
But we do know that cap and trade, if it just applies to point emissions, puts all the onus on one part of the economy, whereas a carbon tax spreads it out more. It's hard to see how to do it without having some application of both instruments.