Why "Giving allowances away for free in a cap-and-trade system and giving (full or partial) exemptions in a carbon tax system are not the same thing"?
"How allowances get handed out matters a lot for the distributional (equity) effects of the policy, but doesn’t affect the efficiency. Exemptions and carve-outs in a tax system, however, make the program less efficient. (The actual carbon tax policy equivalent to free allowances would be lump sum rebates of tax revenues, while leaving marginal tax rates equivalent.)"
Score 1 for Cap-and-trade if we have to do something softer.
From Common Tragedies