Given a choice I'd do LH C over UA C -- I liked LH wines better, LH service seems more customer-oriented, the entertainment choices (music and movies) seem more varied, and (trivial point) I like the color scheme of the LH C cabin better

But maybe I'm biased because of the LH flight attendant who seemed to make it his personal mission to refill my wine glass every time it became empty, and always brought me an accompanying glass of water to keep me hydrated even though I didn't ask for it ^ .
I don't dislike UA C, though. Either one is a reasonable way to get from SFO to FRA.
As far as 777 vs. 747 goes...I like them both! I love going into the upper deck, and especially like the window-seat-side storage bins on the UA 747. But the 777 is actually my favorite long-haul plane to ride in...while the 747 is my favorite passenger jet to see flying.