The question of hiring franchises vs. independent carpet cleaners is always a valid question, but there is no clear answer. The best and worst facility maintenance I have ever seen, as a former industry technical representative, was performed by a ServiceMaster franchisee. The same story holds true for small business people.
Don't use the assumption that a franchise will stand behind you, the consumer, in cases of shoddy workmanship involving a franchisee.
Personally, I like the idea of working with an equipment maker like the two listed below. Both Bane Clene and Host are large family-owned companies, whose customers are generally a part of their removed family.
In the case of Bane Clene, if a customer gets complaints to Bane, Mr. Bane has been known to get personally involved through his customer. Mr. Bane gets personally involved in each customers business by training him, not only the technical aspects of carpet cleaning, but also the business side in bookkeeping and how to be profitable.
Keeping the customer happy is Mr. Bane's principal philosophy and he is one of the father's of Steam Cleaning.
There are more than 35,000 independent carpet cleaners in business today. Most possess honesty and integrity, but you should follow carpet buyers handbook recommendations to ensure satisfaction.