The cove can be a nice dive, but the swells make the vis bad during winter/big swells. I dove the La Jolla Cove many times last summer and enjoyed it. I even did several lobster dives right next to the cove into the Fall. I recently dove a site called Anchor Rock which was about 1/2-3/4 of a mile off the cove and it was amazing! We saw a Giant Sea Bass swimming by. I really enjoy the structure out there. The cove is nice, I'm just waiting for good conditions to dive it.
The shores has extensive structure with areas for the fish to live in. it has several "walls" at different depths to check out stuff. They have 4 different walls: Way North Wall, North Wall, East Wall, and the South Wall. They have fields of sand dollars, large sandy areas the rays, pipefish, moon snails, lizardfish, and crabs love to play in. Sometimes you can even see bat rays (haven't seen too many) They have very large sheephead and an assortment of rockfish which are very cool to look at. It's really a great dive to use your light to check out the small stuff in the holes and in the sand. The more you dive it the more you appriciate the amazing ecosystem you get to visit. At night it can be WILD! The geography has a natural upward progression so if you plan your gas consumption right you can exit in 5 feet of water and 45+ minutes of bottom time and you hit 100 feet max depth... You should check it out sometime. You'll become a much better diver than you would at the cove since you have so much more variety in terms of diving at the La Jolla Shores. It is a diver's training ground! Hope to see you there!