AP. Food, service, and ambience are superb. Did I mention the service is exemplary? Try a slightly later ADR--easy to do since you're staying at WL--since most of the kids and families will have eaten already. You can take in grand nature of the Lodge while sipping your favorite libation in the Territory Lounge before sliding over to AP. Ask to get a window seat, too. I know it will be dark if you get a later ADR, but you can still see plenty.
CG has a reputation for a noisy environment, and as
bicker mentions, its service can be spotty. So far, I've yet to have anything but tremendous service at AP. For example, the first time the wife and I dined at AP, we were having trouble deciding among a few wines to have with our meal (we were doing the wine flight option). Our server brought out a bottle of each wine in question and proceeded to give us samples of each so that we could make an informed decision. We didn't ask, she just did it. The wine list is impressive and encompasses the best wines from WA and OR. There is nothing quite like having a special pinot noir with the signature salmon dish.
After dinner, you can stroll around the grounds of the Lodge, even strike out down the nature trail that follows the perimeter of the lake for a bit. Watch the geyser. Find a quiet spot over by the Hidden Springs pool and just sit and talk. Heck, do a quick change and hit the hot tub over by the Villas. It's quiet and romantic. Honestly, either choice is a fine one, but if you haven't been to AP then you owe yourself the chance to try it out, especially given that you're staying at WL and won't have to drive, bus, or boat to CG. Whichever way you choose, bon apetit! And congrats on your anniversary!
P.S. If you let them know ahead of time, they will make the platings reflect the fact that it's your anniversary, or they'll even do a special cake for you.