On my international trip two weeks ago, I flew on Lufthansa from Chicago to Dusseldorf and United from Frankfurt to Washington D.C.--each way in coach as our business travel budget does not support first or business class premiums.
The Lufthansa flight was far superior:
1) More Leg Room - every inch counts when on an airplane for 8+ hours (especially if you are 6ft. tall or more). Lufthansa coach seats provided at least 2 and maybe 3 or 4 more inches of legroom throughout coach class;
2) Better Audio Visual - movies get me through international flights and Lufthansa's A/V set up is very user-friendly, offering a selection of no less than six feature films which--and this is the important part--are individually controlled (play, stop, restart, paused, etc.) by each passenger. All of United's movies were started by the flight crew and were shown at the same time on different channels (i.e., the passenger cannot choose to watch/pause a movie when he/she desires);
3) Free cocktails - On Lufthansa, I enjoyed a complimentary glass of Riesling and could have continued imbibing alcohol at no cost. United charges for all liquor.
4) Friendlier service - United's flight crew were not unfriendly, but they were certainly not as friendly, welcoming and passenger-focused as Lufthansa's attendants. "Methodical" or "business-like" would be two good adjectives to describe United's service. They went through the motions and seemed anxious to get the flight over with whereas Lufthansa's crew made you feel at home in the sky;
5) Smaller overhead compartments - It's possible United's smaller overhead compartments were due to a different plane (Boeing 777 vs. Airbus A340), but the 777 is not small by any means.
Needless to say, future trips to Germany for me and my family will be booked on Lufthansa.