There's nothing wrong with CO2 emissions, as long as they remain carbon-neutral. So if you capture carbon dioxide from the atmosphere, and then use it to synthesize methanol or methane, then there are no problems with that.

Methanol is slightly preferred because methane can leak, and it's a more potent greenhouse gas than CO2. However, even most of the CH4 leaks happen near the drilling wells, and in pipelines. It's unlikely that synthetic CH4 will have to be transported over long distances.