Ventilation is energetically expensive, and can be even impossible to retrofit (windows that don't open, ...) Purification however is energetically very cheap (just a fan blowing through a filter, maybe with a UV led, no temperature change). And has the bonus benefit of removing other dangerous particulate stuff from the air (dust, smoke, ...)
Air purifiers are very loud and mostly effective at removing particulates. If you want to remove VOCs, formaldehyde and CO2 then ventilation is a lot more effective.
A well designed ventilation system can be completely inaudible.