I think the term SC is pretty out dated these days.
It was a term used decades ago when U.K. based law firms were no where near as international as they are now.
Most of the SC are now prominent international firms, mainly due to mergers with firms in other jurisdictions. Most of them have transformed because of this and actually are all quite different from one another because of this. Because lf those differences, you would get varied opinions regarding reputation/how well known they are based on the relevance of the person’s interests to the firm(s) they are suggesting.