There is another advantage to cap and trade as opposed to tax. With cap and trade, you may have a politically motivated allocation of emission rights initially

There is another advantage to cap and trade as opposed to tax. With cap and trade, you may have a politically motivated allocation of emission rights initially, but it's a one-off transfer and soon enough they end up the hands of the people with the most productive use of emissions. With a carbon tax, people will continuously expand resources in the form of lobbying to try and receive the proceeds of the tax. The government has to stay in the loop forever.