I dunno Arik, it's got me stumped. Best suggestion I can offer is to experiment a bit, start with a new very basic single-light scene and render out on both machines, and keep adding complexity (ie more light, soft shadows, etc) until the problem presents itself.
On closer inspection there are a couple of very weird things in image 2, for example while the shadow immediately surrounding the nearest light is more-or-less as it should be, if you follow the power conduit down the wall to the cylindrical power coupling, the shadow under it is actually reversed, ie is lighter than the background. Bizarre!
BTW, are these both rendered as single uncompressed frames, or as frames from a movie which might be using different codecs?