Thai site Appdisqus attended a Sony launch event for the Sony Xperia Z1, which, with its 20 megapixel camera, claims to offer better pictures than the Nokia Lumia 1020.
Fortunately they had a Nokia Lumia 1020 with them, and was able to put the claim to direct test.
I think from a sample of the pictures captured it is pretty clear the Xperia Z1 is not even in the same class.
http://wmpoweruser.com/nokia-lumia-1020-upstages-the-sony-xperia-z1-at-sonys-own-launch-event/