D600 with D7100 as Back up

I have not heard any Cons on using FX Glass on DX Bodies? I am kind of concern with any possisble IQ degradation??? I have no information to base this concern however. Anybody have any input on this would be appreciated.

BTW I think the D600 and D7100 uses the same Batteries- another Pro, unfortunately they use different Battery Grips - why Nikon????