on my small experience, limited to 2 Moxy in Italy and all the Mercures in the same country, Moxy win easily...not only, as you correctly say, because lobby and common areas are really very nice, but also about rooms (modern, stylish, not smaller, with better amenities)

Having experienced also some Mercures in Asia or newly renovated in Europe, I can say Mercure rooms are better ...and have nothing to complain also on common areas

I have the opinion that Mercure change too much from one country/property to another, so is difficult to compare this brand in its totality, while (I can suppose) Moxys are more standardized