I end up flying with LH a lot anyway, since many of my flights are between Israel and Europe. My question really was, given the above, would it better for me to switch to LH M&M (I guess the answer is yes, as I now realize that airlines do not upgrade Star Alliance gold member, unless they are gold with that airline).

My only remaining question is, is LH (both as carrier and as frequent flyer program) better then any of Sky Team airlines (KLM, AirFrance, Alitalia)?