Originally Posted by
findark
Native flight numbers are always easier.
I agree in general with this and my default would be native flight numbers, particularly since I've had trouble getting seat assignments on LH with a UA codeshare.
My one caveat is that if you're a UA elite (particularly 1K or GS) you will likely have better results calling to make changes before travel has commenced if you ticket through UA. LH phone agents are not particularly pleasant or accommodating, and they're certainly not going to waive a change fee, which UA agents will do pretty frequently.