Re: The Circular Dry Foam Shampoo Method (Encapsulation) used with the Kirby Rug Renovator (since c.1990 called Carpet Shampoo System), Aerus/Electrolux Floor Pro, TriStar FloorStar, et cetera)
Interestingly, both the Kirby and Aerus/Electrolux carpet shampoo systems were introduced in 1965. So, they have been used and improved upon for nearly half a century. They differ in that the Kirby system is attached to the vacuum cleaner and uses a brush cylinder while Aerus/Electrolux's method uses a separate triple-brush machine with rotary-action brushes.
I have successfully used the two methods and therefore find value in both. Ideally, they would be used interchangeably to maximize their pros and minimize their cons. Furthermore, they are most effective when ongoing maintenance and care are given (e. g. frequent vacuuming, use of entrance mats, removal of footwear, immediate treatment of soils and spills--with a clean cloth & spot remover or machine).
There are more types of carpet cleaning methods than the two you mentioned, but I will just focus on them.
Pros I have read ...
Extraction method:
1) More disinfecting qualities with hot water and shampoo
2) Extraction of solution with same machine (immediate recovery)
3) Carpet fibers are rinsed with water
4) Some contain brushes to agitate carpet fibers
5) Some contain nozzles for dispensing concentrated solution for stains or spots
Encapsulation Method
1) Disinfecting, brightening
2) Dust and dirt particles are encapsulated in shampoo and left to crystallize rather than creating a sludge
3) Extraction of crystallized dirt removed by vacuum cleaner (no recovery tank to empty)
4) Does not involve the use of toxic chemicals
5) Very effective in removing dust mite allergens and mold allergens
Cons I have read ...
Extraction Method:
1) User error--not following directions in the owners manual.
2) Not spot cleaning soiled areas in a timely fashion and/or not pre-treating them before extracting.
3) "Shoots" water into carpet base and pad creating a sludge that can't be completely removed
4) Possibility of over-wetting carpet leading to mold and mildew growth, delaminating, and/or shrinkage of jute
5) Not environmentally-friendly (e.g. much water and--sometimes--toxic chemical use)
Encapsulation Method:
1) User error--not following directions in the owners manual.
2) Not spot cleaning soiled areas in a timely fashion and/or not pre-treating them before encapsulating.
3) Possibility of leaving carpet fibers sticky if solution is improperly mixed, over-applied, or a vacuum with poor air flow is used.
4) Possibility of wearing out carpet fibers by using brushes meant for hard surface cleaning or by going over areas with too much pressure or too many times.
5) Results can vary depending on the quality of brushes and/or dry foam shampoo
Extraction and Encapsulation Comparison Chart:
http://www.excellent-supply.com/Comparing-Encapsulation-with-Hot-Water-Extraction_b_10.html
Here is a link that provides an informative and unbiased overview of different carpet cleaning methods:
http://www.apex-carpetcleaning.com/ourservices/carpetcleaningmethods.html
Here is some information on the history of carpet cleaning in the 19th and 20th centuries:
http://www.burrows.com/carpetcleaning/