In today’s world I would say LH all the way.
Think about the craziness of not having separate FTLs for short-medium and Long Haul ops.
On LH (the real one not a mix like in EK or so) with 3 or 4 trips a month you end up with 80/90 hours and 13/14 days off. Yes jet lag can be a factor but personally I believe it is way less tiring than flying 5 or 6 days in a row for a LCC when you start day 1 with a 3 am wake up call and en on day 6 with a 2 am checkout. That is jet lag too.
On LH as long as you take enough time to rest and only go out on layover when you have recovered than it becomes really smooth. A lot of people get fatigued because the end up in LAX, sleep 3 hours and go out. Of course you will end up fatigued and blame jet lag. If you do things properly it’s great. Plus working in Europe mainland you don’t land from a 10 hours LH flight at 7 am and go out for a Gulf turn around again at 1 am…