Under the system of carbon tax, incredibly wealthy companies can simply attempt to compensate for their immense environmental damage by throwing money at the issue, a substance that in no way is capable of reversing the climate crisis we are facing, even IF that money gets funnelled directly toward environmental conservation (which it isn't). A cap-and-trade system recognizes the inevitable limits that already exist in the natural world, and then encourages companies to work amongst themselves to find a balance for the need of carbon emissions between industries. If one industry MUST produce a certain amount of carbon, that allows another industry that either does not, or was clever enough to come up with a work-around in their production to monetarily benefit, while the other industry still has the ability to survive.
No, cap and trade does not better uphold democratic principles, because cap and trade hands a monopoly of the market of carbon emissions to certain producers. The democratic way to let everyone who wants to enter a market and compete for business the opportunity to do that. Limiting the number of players is socialist, not democratic.