Normally, I fly DL exclusively, but over the past two years I've taken about four LH trans-Atlantic flights because of the better price. I must say that I was extremly impressed with LH each time. My reasons:
(1) In Coach (if your flight is on an A-330 or A-340) you have an individual IFE screen. On the DL B-767 you still look straight ahead to the one screen for the entire cabin.
(2) I found the seats much more comfortable and the food far better (if that's even possible for airline food).
(3) While DL has a good BE product I think LH's is much better.
(4) LH is efficient and I've always found the attendants gracious. DL gets mixed ratings on this of late.
(5) LH has newer aircrafts crossing the Atlantic which I find much more comfortable and pleasant to fly.
So, enjoy whichever flight you end up taking for your trip. That's just my two cents!