Although I normally sail out of Kemah on the shores of Galveston Bay, My Tiburon 36' ketch is at the moment in Port Aransas. Comparing Galveston and Corpus Christi Bays, it depends on what you want. There is more deep water in Corpus Christi Bay, but there are spoil banks along the ship channel and ICW that you have to watch out for. Galveston Bay has plenty of reefs and shallow areas, and there are spoil banks adjacent to the Houston Ship Channel and the ICW there as well. You're more likely to go aground in Galveston Bay than CC Bay.
Water is prettier in CC Bay owing to the sand bottom. Winds are generally higher and more regular than Galveston, but there are few protected anchorages. The view of Corpus Christi is beautiful! Local tourist attractions include the replicas of Christopher Columbus' fleet, USS Lexington, and the Texas State Aquarium (nice, but not "world class"). Port Aransas is a funky town with good restaurants, a nice beach, and lots of atmosphere. A nearby place to visit is Rockport, which is the site of the Texas Maritime Museum, and if you're into wildlife, lots of birds. Not far away is the Aransas Wildlife Refuge which is the winter home of the world's population of Whooping Cranes.
If you're planning to go to Mexico, Corpus Christi is, of course, about 200 miles closer. If you go down the ICW, you'll share the water with fishing boats, towboats and barges, and the spoil banks are unbelievably shallow. Not much to see either; on the land side are mostly ranches (the famous King Ranch takes up a lot of the trip), and Padre Island is happily undeveloped.
Once you go outside, the Gulf is about the same in either location. Much more big ship traffic in the Galveston Bay area; there are similar numbers of oil platforms off both bays.
One of the best things about cruising in the Houston/Galveston area is the incredible infrastructure devoted to boating. There are many excellent marinas and boatyards, and you can get just about anything you need for your boat in the Clear Lake area. Corpus Christi doesn't come close in that regard.
S/V "Southern Cross"