For most things LHR duty free is cheaper than MUC duty free, whenever I've checked. Rarely worth the trouble to carry liquids from MUC-LHR if you have time to shop at LHR (and you should, it is structured so that almost all gates require walking through or past the duty free shop -- LHR is actually a shopping mall that happens to have planes land and takeoff there occasionally, hence the lack of investment in doing things like clearing snow from runways).