If a carpet cleaning business has been around for a long time, does that make them the best at what they offer?

Not necessarily.
Some of the established carpet cleaning businesses brag about how long they have been in business but this can sometimes be because they are a franchised operation which has operators and franchisees come and go as they either finish their contracts or in most instances forced to hand the business back to the franchisor.
New businesses will tend to ensure that they select the best equipment and adopt the latest cleaning technologies in order to stand apart from the established brands.
Small businesses will also usually be run by the owners who have a vested interest in ensuring that the customer is happy enough to pass on compliments to their family and friends.
Please try some of the smaller businesses and you may be pleasantly surprised.