Cheaper to first concentrate the CO2, then pressurise it.

Pressurisation takes a large energy input to pack down the gas into a small volume. A lot of heat occurs as a by-product (P=VT - ideal gas law, plus non-ideal and frictional effects).

You don't want to be pressurising the bulk atmosphere to remove 350 ppm of CO2.

It's best to start with a CO2-rich gas source such as the chimney of a power plant. Techniques such as reverse-osmosis membranes represent the most cost-effective mechanism of concentrating a *VERY* CO2-rich gas stream to then deal with.

(Did you know that small stand-alone CO2 plants produce dry ice and bottled CO2 by the simple expedient of burning hydrocarbons to make CO2-rich exhaust gas, then concentrating the CO2 and using the energy of combustion to compress the gas and liquefy the CO2. (you use an infernal combustion engine to do the burning and pumping together).)

(Solid CO2 is produced by passing the liquid through an expansion nozzle. 30% solidifies and 70% expands to gas, cooling the system adiabatically. Then you recompress the 70% and cool it and recycle...)