The very short answer
The Experia Z's camera doesn't come close to a professional camera. Yet it does take awesome pictures and is great for taking some photos while on the go. It's basically as good as one of those small compact cameras. So no fancy arty photos, but good vacation photos.
Where is falls short
Less control
Even though the Xperia z gives you a lot of options, there are still some missing. You can change your exposure value, iso, white balance and a lot more, though I couldn't change the aperture. Nor can you use any lenses, of course this it true for pretty much any phone-camera, but it's still something I missed.
(Some fun with a fish-eye lens on a Canon 550D on the right.)
No hardware button
Like the title says, there's not hardware button to take pictures. You can zoom by using the volume buttons but to take a picture you'll have to touch the screen.
Where it excels
Features
Even the default camera app has a lot of them. There's an awesome panorama mode, which works great but can be a little blurry sometimes. Also there's 'Smile Shutter' which takes a picture when everyone is smiling. It even adds a meter next to everyone's face telling you how hard they're smiling which is really funny. And of course you've got a timer, geotagging, image stabiliser, flash and HDR. On top of that there are also a bunch of focus modes: face detection, object tracking, touch focus and mid-screen auto focus. And it all just works.
Ease of use
The Xperia Z also has a 'Superior auto' mode which just does everything for you. It'll try to put everything just right for the current conditions, and does a good job at it too.
Not good nor bad
Quality
The Xperia Z's picture quality is average. It's really good when looking at it on the Xperia Z, with it's fancy Bravia technology. Though when I looked at the pictures on my computer the quality was noticeably worse, still not horrible, but worse.
Here's a small part of a 13MP photo, so you can see for yourself:
Conclusion
I really like the camera, it has everything I need. It takes simple pictures very good and without bitching about settings, yet gives you the option to change them if you would want to.
So that's the camera, hopefully till next time!