And if not exclusivity, they likely both have the standard anti-moonlighting, broad IP assignment clauses that we have all come to love: "Anything you produce using company equipment or your own equipment, on company time or on your time, belongs to us." All jobs I've had for the past decade come with something like that.

This was has been my experience with other firms like IBM. I remember it being stated in my employment agreement that I needed permission to work a second job. It even limited your open source exposure. Whether it could be legally enforced is a different matter.