I work at one of the bigger outfits and house rules vary but as far as I am aware, maximum group size varies from 8 to 10 divers per guide. On busy days this is a regular occurrence and I can tell you for a fact that some of the smaller operators do this also, because I've counted their divers as they swim directly through my group!
With the smaller operators, you may well find you are in smaller groups, simply because they have less business, but they often have to share boats with other centres, and you may not be able to pick which location you visit every day. The big centres can usually offer daily trips local, or to Tiran or Ras Mohamed, whereas smaller centres offer only one or the other.
Some dive centres will allow certain experienced divers to dive independently (in a buddy team, of course, never solo), and the level of independence varies with overall experience in the Red Sea. Some of our guests have dived in the Red Sea - with the same centre - for 20 or 30 years, accumulating hundreds of dives in the process, and I'm not going to insist that they stick with the group as long as they stick to the overall plan for the day. It is unlikely that 40 dives will earn you that privelage in Ras Mohamed or Tiran, but they may allow it at some sites if you prove yourself to be a good diver.
We (as in the big outfits) all try to keep our divers in groups with similar experience levels and ensure "insta-buddies" are partnered with the most appropriate buddy-less diver on the boat, but it's not always possible and yes, sometimes end up having to look after their buddy a little bit, but a lot of divers actually enjoy that responsibility.
It is not 100% true to say that the bigger outfits have more experienced guides, but it is generally the case that you will find the most experienced Sharm dive staff at these centres, although there are small, independent centres of excellence.
As always I add my standard disclaimer that I am not promoting the big names simply because I work for one of them, but we've been doing it for a long time now, and do it very well, and the customers are (mostly) extremely satisfied with the service received. And as always I offer my standard advice. Most dive centres have a website or at the very least an e-mail contact so get in touch with the centre, let them know what you want and ask what they can offer in return, and I agree with interceptor - build a dialogue.
Wherever you go, I hope you enjoy your time here!
Cheers
C.