I have already made several posts on this, but I want to focus on two points regarding this and apologize that some of this will be repetition. One is theory and one is on the views of economists.
The theory point derives from Martin Weitzman's 1974 paper in the Review of Economic Studies on Prices and Quantities. I mentioned this argument in my Pigou Club post, but again, in a world where we lack certainty about impacts of trying to clean up, whether one focuses on fixing prices or fixing quantities depends on the potential threat from getting it wrong. So, if one is more worried about overly high costs of cleanup from being wrong, then one wants to avoid that by fixing prices, which in the environmental policy debate means taxes or some similar mechanism. If one is more worried about getting the benefits of cleaning up wrong, that is having a disaster because one did not keep the quantities controlled properly, then one should use a quantity limit approach. Personally I think the latter is by far the biggest problem for the global warming problem, so a quantity approach is the better way to go, making it cost effective by adding cap and trade or tradable emissions permits to it. I note that a hybrid policy is possible, allowing one or the other to be dominant, but allowing a kick-in if things get too extreme on either side so as to allow the other policy to then also be used.
This would seem to be a strong argument, and I note that Weitzman has largely stayed out of being publicly involved in the debate over taxes versus cap and trade at Paris, although he is in the same department as Robert Stavins, who has supported cap and trade pretty clearly. However, as many have noted there are some very prominent economists in the Pigou Club, with Arrow, Schelling, and Stiglitz the most prominent, and with Mankiw also very promient. More than one observer has said, "how can you disagree with these guys?" Well, for starters, I do not think any of them have said that one should not or never use cap and trade as climatologist James Hansen seems to have said after the Paris agreement tilted for cap and trade as I predicted it would based on past diplomatic and political history, although Paris certainly allows nations to use carbon taxes to achieve their national goals if they so choose. The only favoritism is for international coordination, where the agreement suggests that trading permits is a useful way to do that, which it certainly is.
As it is, I see this as partly a debate between very famous economists whose principal areas of research are not in the economics of global warming, although this topic has become Schelling's main concern in recent years, and I think that both he and Arrow also know a lot about the climate science involved, against some economists whose main field has been environmental economics, and thus are not as well known publicly as these Nobel Prize winners. Stavins is one of those, and so is Weitzman (although he has publicly remained neutral). I shall name another, Tom Tietenberg of Colby College and J.H. Dales, whose current location I do not know. Dales was the actually the first to propose tradable emissions permits, aka cap and trade back in the 1960s, getting the idea from the Coase Theorem, which was developed very much as a critique of Pigou's approach to taxing negative externalities. I may not be right on this, but I suspect that part of why Arrow and Schelling and Stiglitz have favored Pigouvian taxes is that it was the earliest approach formulated and the only one in all the textbooks for years, dating back to the 1920s.
It was Tom Tietenberg in the 1970s who led the actual first implementation of cap and trade, the Wisconsin plan to limit BOD emissions into the Fox River, which I was peripherally involved with. But Tom was the main person, and he is also the author of the most widely used environmental economics textbook. He went from Wisconsin to be one of the main people advising EPA and the US government more generally on implementing the successful system for trading permits for lead in gasoline and SO2 emissions, much praised by Schmalensee and Stavins in their forthcoming JEP article. But nobody outside of environmental econ knows who Tom Tietenberg is, and, of course, the cap and trade system arose initially out of an effort to make cost effective the quantity limits laws that the US had put in place in the early 1970s against the advice of all the economists supporting Pigouvian taxes, many of them signatories on this petition that went to Paris.
My final observation on this is that this reminds me a bit of what happened after the fall of the Soviet Union. There were a bunch of comparative economists around, not well known outside of their field, who knew very well how difficult the transition processes would be and cautioned about overly ambitious plans brought in from the outside in a "one size fits all" manner. But all the pizzazz of the fall brought all sorts of very well known economists who had not studied comparative economics into the ball game, getting ahold of the policy apparatus and developing and enforcing the destructive Washington Consensus, which led to many disasters in Eastern Europe against the advice of many of the more established but less well known comparative economists. This reminds me of that a bit, the advocates of carbon taxes pushing a textbook ideal against a policy actually developed by environmental economists that has much more going for it, especially at the global level.