I was using the Z Ultra the other day, the way it's designed (Omni-balance) really helps the device nicely in terms of completely even weight distribution, which made it feel lighter than it was, so I'm looking towards that in Z1.
G2 has OIS, but I'm not entirely sure what Z1 has, all I know it's SteadyShot technology -- and based on the video here
https://www.youtube.com/watch?v=pslULskIYkU -- (Z1 image stabilization testing) -- whatever Z1 has is no slouch either, in fact, I think it looks better than most of the other phones that I've used with OIS (HTC One).
The bezel is a personal preference. To be honest, I think having a balanced bezel makes the overall design look nice.
Edit:
http://en.wikipedia.org/wiki/SteadyShot
When a camera is operated hand-held, the operator's shaky hands cause instabilities in the captured image stream. SteadyShot technology works inside the body of the camera. It uses motion sensors to detect the user's movements. SteadyShot then compensates for some of these movements, in some versions by moving the optics and in some versions by moving the image sensor in an opposite direction to the movement.
This approach is contrasted to digital image stabilization in which the physical image is allowed to "track" the scene on the CCD by software to produce a stable image. The digital technique requires the pixel count to be increased to allow the image to move on the sensor while keeping reference points within the boundaries of the capture chip.
Maybe that explains why there is a lack of actual OIS?