Within Star Alliance, the question of which airline to fly and the question of which FF program to use are almost entirely independent.

You might, for example, find it best to stay with Miles & More while patronizing BD and UA. Or you might decide to fly LH and credit your miles to UA's Mileage Plus. (I've done both in the same week.)

I suggest choosing an airline each time you need to fly, but (unless you are racking up several hundred thousand miles per year) staying with just one FF program. Which *A FF program is best for you will depend on which airlines you fly most, the length of your segments, the fares you pay, etc. M&M is particularly good for those who pay First and Business Class fares and for those who fly short segments.