These two approaches are often presented as rivals when they are really complementary. One goes deeper; the other returns the space to use faster.
Choosing well is a matter of fibre, soil level and how quickly the room must be usable.
Hot water extraction
Extraction flushes soil out of the pile with hot water and solution under pressure and recovers it, reaching deeper into the fibre than surface methods.
The trade-off is drying time, which makes it best suited to domestic deep cleans, heavily soiled carpet, end-of-tenancy work and out-of-hours commercial cleaning.
Low-moisture and dry compound methods
Low-moisture systems use encapsulation chemistry or absorbent compounds worked into the pile, then removed by vacuum. Drying is measured in minutes to a couple of hours.
They suit interim maintenance, moisture-sensitive fibres, occupied offices and anywhere that cannot be closed off.
Using both
The most cost-effective long-term approach in commercial settings is frequent low-moisture maintenance in high-traffic zones with periodic deep extraction across the whole area.
In homes, extraction is the usual choice, with low-moisture used where fibre or a tight timescale demands it.

