It's VERY rare that it's ever cheaper to fly on another airline instead of your own. I know you have to if your own airline doesn't fly to your final destination, but it's better to do that for the short-haul if you can.

I would imagine that FRA would be a better gateway to eastern Europe, and since US and LH are both star alliance, you've probably got a ZED low agreement with them. And Star Alliance tend to give each other better priority, too (I know that UA gives *A employees the same priority as UAX employees)