I stay away from debating whether regulation or taxes beat cap and trade on limiting CO2 emissions, because I don't think it is something to be settled theoretically. Or -- worse -- speculatively, say, on the grounds that we distrust markets more than we distrust the state. Or vice versa. As far as I'm concerned, both markets and the state are undesirable, because we collectively can't control them effectively. So, we need to disolve them, which can only result from a long series of revolutions. So, for the time being, the issue ultimately boils down to empirical measure and -- on the practical side -- a lot of trial and error.
The general theory appears straightforward to me. Well, kind of. Paul Krugman recently wrote in his blog that cap and trade and Pigouvian taxes (or subsidies for that matter) are essentially equivalent. I think he meant it in the following sense:
If you know the supply (or marginal cost) and demand (or marginal benefit) functions, private and social (i.e. without and with the external effects), then you can always determine the socially optimal level of CO2 emissions, level that you can then split into shares and allocate them to people, who can then trade them in a market. If people follow the script of their market functions (i.e. if the assumptions that underpin market functions hold), then the amount of emissions would be capped at the socially optimal level.
Similarly, if you know the supply and demand functions, you can always determine a Pigouvian tax (or subsidy) to induce producers to reduce emissions from the privately optimal level to the socially optimal one. All is required is setting the tax (or subsidy) at an amount equivalent to the size of the net external cost at the privately optimal (but socially inefficient) level of emissions. That forces emitters to internalize the net external cost, who then willingly limit their production to the socially optimal level.
Quick and dirty actions to solve practical problems beat no action at all in the hope that a perfect solution will fall from the sky. The practical experiences of taxation and cap and trade need to be studied very carefully -- something I've not done. But from afar I can see a few thorny practical issues, even if measuring the level of emissions were simple:
How on earth do you determine the private and social supply and demand functions? For example, the location and shape of estimated supply and demand functions is highly sensitive to the period of time considered. Basically, choose a sufficiently long period of time, and you can always make the elasticities arbitrarily large. With arbitrarily large elasticities, very tiny taxes (or subsidies) would -- in theory -- do the job. So, what is the relevant period of time? This wrecks all approaches, including plain regulation (i.e. telling emitters how much CO2 to emit, period). And this is separate from the technical, empirical issues of estimating market functions (well, their elasticities, from which you can integrate costs and benefits).
Another issue I find daunting is that supply and demand, private and social, are continuously shifted by a bunch of factors without prior notice: technology, consumption patterns, prices of virtually everything else. Basically, a perfect regulator would have to re-calibrate dynamically, continuously (or at least with such frequency that the benefits of recalibration are not offset by the associated transaction costs), the socially and privately optimal levels. Otherwise, there'd be garbage-in garbage-out with any of the approaches.
Then the practical issues of administering the approach, in the face of the profit motive, the incentives of public servants, the motivations of the public, etc.
By the way, I haven't seen anybody challenging what I believe is a fundamental presumption under cap and trade as is, namely that the national shares of allowed CO2 emissions are to be allocated to the emitters only. (Am I right that this is the presumption?) I'd expect to hear left-wing economists denouncing this as sheer theft. The rights of ownership over the atmosphere are assumed to belong exclusively to the main CO2 emitters? How about the rest of us? To start with, I would expect cap and trade allocating permits to everybody following a simple egalitarian rule: one (equal) share per person. We can then decide whether to trade it in the market or make origami figures with them.
I'm sure that something like this would be easier to implement than land reform in Mexico. If it worked, we could then confidently extend the practice to the myriad of other net externalities resulting from capitalism -- environmental and social. For example, if manufacturers produce gadgets along with garbage and sick workers; if TV, Frito Lay, and Pepsi produce pleasure along with stupidity, obesity, and consumerism; if banks produce whatever they produce along with crashes that ruin our lives; etc., then as rank-and-file users of the natural and social environment, we are entitled to the same allowance of permits to destroy nature and society as everybody else.
It would not be the end of markets and the state, but at least we'd be talking!