For a simple FRA-HKG, I would do LH (especially if you have not done the FCT before - definitely something to tick off the list).
CX lounge at FRA is very, very mediocre, and personally I prefer an evening departure if possible. On CX's daytime departure, you will arrive in the morning so getting through the day can be a real drag, whereas flying LH you can eat well in the FCT and sleep onboard, and wake up early enough so that you are tired in time for the evening in HKG.