Yeah I am doubting those battery life claims also. I have two Sony AZ1's the battery is slightly smaller than the AS200 but it is about the same capacity. I have to carry extra batteries with me if I plan on recording anything in HD and want more than about 1:45:00 of recording.
The anti-shake is a great feature and works very well. I also like the fact that, at least in my opinion the Sony's have much better image quality and definitely have better low light performance than any GoPro (I also have a GoPro Hero3+Silver).