Hi there, it seems to me the main differences between the two are:
The Big Shot/ Big Kick has a slightly wider opening so will take wider dies/folders
The BS/BK has a larger footprint, which means it will take up more space, BUT it does mean it won't move around in use. I find you need to hold a bug still while you crank it.
I believe the BS/BK will take thicker dies than the Cuttlebug will.
When I had the opportunity to upgrade from my 'bug, I actually went with a
BS Pro . I'm fortunate enough to have a whole room of my own for crafting, so the space it takes up wasn't an issue. It was a 'once & forever' type upgrade. The opening on it is 12" wide, so I figured that I will never need to use a die/folder bigger than that!