Share your experience!
To put it simply -- Does the Z1's camera have hardware image stabilization of some form?
The whitepaper simply describes the feature of "image stabilization" for the camera.
The website goes a step further and discusses the SteadyShot feature for shooting video, but makes NO mention of SteadyShot when it comes to taking photos.
The disparity between the two is somewhat confusing as to what is actually there. According to Wiki and Sony websites, there are a few types of SteadyShot that Sony utilizes in its cameras (both still and video).
1) Does the Z1 have SteadyShot technology for taking photos?
2) If so, which type of SteadyShot is being used?
3) Which type of SteadyShot is being used for video?
Thanks 
Most likely it will be like the Image stabilization found on the Z series.
As per as my knowledge and what I get from different video reviews
Xperia Z1 did not have optical stabilization (hardware stabilization). But it is better than the Xperia Z or previously released Xperia phones, question is how?
Answer is Xperia Z1 have Five lens in its camera that named G lens which help the Xperia Z1 to zoom up to 3X without losing performance like optical zooming.
And the same G-lens and Bionz processor together help Xperia Z1 camera to stabilize the photos and videos, this stabilization is better than the digital stabilization.
I believe Sony's top teir cameras use the same type of stabalisation as the XZ1 to great effect, there have been several videos posted around the net that demonstrate this and it really is very good