First of all, we should note that cap and trade programs could be used under the Kyoto Protocol. So it is not really right to present these as alternatives to one another.
In general, a cap and trade program would work better than government regulations that tell firms exactly how to reduce emissions. This is because the private sector is always going to be more innovative than the government. If we have a cap and trade system, every firm has an incentive to invent ways to reduce its emissions. They will hard to figure out ways to do so that will be the most efficient. This will reduce emissions more than would be the case if the government simply came in and told manufacturers to use specific technologies to reduce their emissions.