I have a lot to do with the domestic cleaning industry in the UK and it seems that there variable quality of service to be found from either model.
With a company it just depends on thei business model and how the staff are obtained, trained an managed.
Solo cleaners seem to be deemed more unreliable and seem to be found to be more unprofessional in a lot of cases, some are not even carrying insurance which when you go into someone's home and handle all of their items as cleaners must is essential but on the flip side if you do find a good one they can be just as good a s trained staff of a company and often at half the price. Some solos will refuse to take responsibility - but not all! Find out about how they operate their business before you hire.
We own a domestic cleaning company as well as our industry involvement in general but it is a private company not an agency, the reason our clients say they will pay a lot more for our service and don't mind the costs involved being double what they used to pay in some cases is because they have had bad experiences with solo cleaners before so they understand the benefits of having staff managed for them and the service as a whole taken care of for them.
Also, of course we've had a few clients come to us from other companies who have also caused them dissatisfaction in some way so it works both ways.
At the same time it has to be considered that of course the clients who come to us have had bad experiences with their previous service provider or they would not be speaking to us for a quote if they were happy and settled with their current supplier. Some clients have tried a few different options before they settled with us, we hear it all! Also, in the odd case it then turns out that we also are not a good match for them either and that's fine too.
It all boils down to the fact that you just have to find the best match to suit your own personal needs, be that from a solo cleaner or a company. It's a highly personal service so take a bit of time and do a bit of research, read their website or fb page, whatever they use for marketing and see if what that person/company is a good fit for your needs. Once you find something that fits you, the relationship often lasts for years.
Make sure that both yourself and the service provider agree right at the beginning about the expectations from either party and make sure this agreement is clear. Some better companies (and some solos) will put a service list in writing for you so you'll know that these jobs are included within the price quoted and can be clear on what their service does and does not offer for that price.
As long as they are able to provide what you personally need and conduct their business professionally with insurance etc in place that's the main criteria rather than independent vs company.