Norfolk. AFAIK, Portsmouth doesn't "do" carriers at all.
Norfolk Naval Shipyard is indeed in Portsmouth, and they do service carriers. It's an impressive sight, watching them squeak their way up the Elizabeth River past downtown Norfolk.
My earlier pic was shot from the middle of the Elizabeth River, from a little powerboat that had no special privileges. Without going into detail, suffice to say that within a certain range the boat would have been reduced to confetti in a matter of seconds.
I remember the Captain of the Big E ran her a ground in SF Bay about 18 or 20 years ago. I believe he is still counting penguins in Antarctica.