The LG G2 and the Nokia Lumia 1020 both feature Optical Image Stabilization (OIS) which eliminates camera shaking and results in blur free photos. Check out the following test video which compares both cameras head to head and see which one is best.
|Optics/Sensor||1/1.5", 41 MP Carl Zeiss||1/3" 13 MP|
|Focal Length||27mm (4:3); 25mm (16:9)||29mm|
|Image Stabilization||Optical Image Stabilization||Optical Image Stabilization|
|Flash||Xenon + LED||LED|
source - All About Windows Phone