Award levels for both programmes are the same but of course with LH M&M, you'd get the required levels much faster than KF.
KF occasionally has special promos that give you bonuses or discount on award levels that are worth looking at over M&M. So you'd just have to read up on your newsletters to determine which programme is better on which routes.
If you are based in SIN and use AMEX or the various creditcards, then you can bank miles to KF and use them that way.