2 great options. Not really a bad choice here.
For the outbound, as you depart FRA on TG, you miss out on the FC Terminal and MB ride to the plane. Still a nice way to travel, though.
For me, it would come down to which schedule is a better fit. Typically, the European route is an evening departure from USA with an early morning arrival in BKK. Through Asia, it is an early AM departure from USA and late night arrival BKK. I assume your itinerary is the same?
I like the European route when I want to get in a day of work, then head out on holiday in the evening.
Sounds like the Asia routing is faster overall (shorter layover?) and there is the novelty factor of a new airline in F.
Is this a round trip? You could try NH on the way over and LH for the way back...