For weddings, I use full manual exclusively. I've been tempted to use aperture priority a few times outdoors, in wildly varying light, but my manual shooting is getting better as I learn to constantly monitor the meter and histograms.
I'm not saying the "semi-automatic" modes aren't good or that they shouldn't be used, but in most wedding photography (in my experience) you need absolute control over the camera - any guessing the camera has to do is an opportunity for the camera to get it wrong. If you're in a setting where you can trust the automatic settings, or at least you can check on the automatic settings and adjust them and take the shot again, then they are fantastic to use. If you're in a situation where the photo has to be as good as possible the first time with no time to retry, then learning to wield the camera in full manual is the way to go.
I haven't even used the Auto ISO feature on the 5D3 yet. I know I can restrict it to a specific range of values, but I think that I should be able to set the aperture, shutter speed, ISO, focus, framing, and composition at the same time. It's exhausting and sometimes daunting, but when it's done right, it's the best way to consistently get great photos.