Two different kinds of place.
Cobalt Coast is at the North End of the island, small, quiet, self contained and maybe 10 miles away from the Georgetown activity. Very good dive op ( Dive tech ) and outstanding shore diving if the seas are calm enough.
Sunset is much larger, close to town, has an OK dive op and OK shore diving. There is a great open air bar on site so there is lots of action. Cathy Church School of Underwater Photography is also on site if you are interested in photo or video courses. She is a wonderful teacher and person.
In November, there tends to be a fair amount of wind and waves from the North so the North wall and the CC shore diving is often blown out. Not the end of the world, as they will move their boats to the leeward side and bus you over and back. Also, they have a good shore dive site just south of the Turtle Farm at Lighthouse Point, which is sheltered. I like CC personally so I tend to stay there. If you want some other activities, however, I would opt for Sunset. You cannot go wrong either way.
For July, the winds tend to be lighter, the shore diving at CC is excellent and the Divetech boats will have quick access to the North Wall. Sunset does some North Wall diving but their focus seems to be on the West which is OK but not quites as good diving.
Another option would be to rent a condo on the North end of Seven Mile Beach. Christopher Columbus and Discovery Point are pretty reasonable and rental rates will be lower in July, rent a car as well and do it all. Most of the dive operators will also pick you up in the AM for their boat dives and they will all provide a package price whether you stay there or not. Sunset and CC packages both include unlimited shore diving as I recall. ( I don't think Sunset Divers picks up but I could be wrong on this.