I fly both LH and UA a lot.

In F, the service, food, and wines are significantly better on LH. The seats, however, are a LOT better on UA. You just cannot compare a suite on UA to a 2x2 seat, albeit lay flat, on LH. LH seats are ok if traveling with someone you know and want to sit next to, otherwise, forget it. That's not first class. It's a business class product.

In business, right now, United comes out ahead. The seats are much better on UA and the food/beverages are only a little better on LH. However, LH is introducing a new, lay flat, business class product. What is funny is that it looks just like the first class product, and there are no announced plans to upgrade the F seats. When that seat is available, LH will be ahead of UA.

UA lounges are far better than even the First Class/Senator lounges on LH, which are pathetic. Ground handling on LH is non-existent. Boarding, particularly in Germany, is a free for all (think April 30, 1975 in Saigon).