If I can save 10 tons of co2 at a cost of 2 dollars and you can save it only at 4 dollars, then if we have to lower the amount by 10 tons with a tax that is evenly distributed the total cost is going to be 3 dollars - 50% more than under a cap and trade system, where I sell you 10 tons worth of co2 credits and implement all the changes.

Since ultimately a carbon limitation is going to mean more expensive products, it is important to limit it as much as possible.

Also I don't see how a cap-and-trade system is going to be more difficult to enforce than a tax, you are still going to have to check if all the companies have paid their taxes.