I haven't had the opportunity to fly New First so I can only compare LH to BA old. Having said this:

- better seat on BA (if it does not fall into bits and pieces)
- more fancy food on LH
- more down to earth food on BA
- by far more international IFE on LH (you English speakers will not care).
- more consistent product on LH
- better ground service in FRA and MUC compared to LHR
- easier to transfer in FRA, DUS or MUC compares to LHR
- No bus gate #10 like in Heathrow.
- LH staff is better in languages (I know, most of you do not care).
- BA has better lounges at outstations.
- BA is waayyyy cheaper....