I have had both single and dual chamber softeners and would only ever buy double-chamber, even though they cost more.
As you know, softeners need to regenerate every so often. Double-chamber ones use alternate chambers and regenerate one whilst the other is in use. The water NEVER goes hard because the regeneration takes less time than running a cylinder to needing regeneration. Single chamber models use various tricks to decide when a regeneration is needed, from simple time dependent to a clever computer program which monitors your usage to predict when the regeneration will be necessary. Whilst the regeneration is taking place any water used will be hard, so the regenerations are usually timed to take place in the night when there is probably) no water being used. Unfortunately prediction is not fool-proof (come back from holiday, wash car, wash clothes etc after not using any water for weeks). If the water runs hard it gets into your header tank and can take days to clear, so hard water showers until then.
Installation of either type is simple, easily within the abilities of a DIYer.