I booked the flight through United. The trip to Munich was United economy plus which was much better than economy. I am only 5ft 1inch so I don't need leg room but the seat reclines more and it is not so cramped.
The flight back was on Lufthansa. The seats are much more comfortable and it seemed just as roomy as economy plus on United. The food and service were very good. The movie system was easy to use. My issue was with trying to get an assigned seat. I had to pay $55 to get an assigned economy seat. Upgrading to economy plus wasn't possible. Apparently there is a bidding system 23 hours in advance but I was never allowed to use it on my phone or computer. Maybe due to booking through United. Very confusing system. Neither United nor Lufthansa could help me.