I cross train at sister-dojangs all the time. But it's with my best friend (she works at one dojang, and owns the other). And, of course, it's the same system, but she teaches totally different than my instructor here. Well, she has her own way of teaching the system. I think it's good to get other points of view, even if it's within the same system.
When I was in TSD, I trained at sister dojangs, AND at a few non TSD dojangs for fun. My old instructor didn't mind if we did this or cross-trained. He also invited other dojangs to attend clinics at our dojang. It was fun to work out with other dojangs/styles.