The key is to do both because they are principally coupled and nothing happens as long as consumers and corporations just point at each other and use it as an excuse to keep on going like before.
Of course you are right that the focus should lie at changing CO2 output at the producer side because the influence is much more focused there. N my opinion it is also dangerous arguing that the companies only supply what the consumers want because that statement is based on the consumption and is biased too much by what the companies offer and at which price. Consumers usually socioeconomically do not have the choice to buy a product at 1.5 times the price, even if they would prefer it for environmental reasons while these companies have immense profits and can and must afford to reduce and finally stop emissions.