I would say the GM since you said she's meaty.
Big bags do make you looks smaller (:
I did not think there was a big difference between the MM and GM for me personally. I got the GM because I could use it for so many other ways than just a purse (which I do use it everyday as well) but now its a bag for many occasions and I have no regrets at all.
thats such the sweetest thing to do for ur sister!!! im actually thinkin of gettin the same one for my sis as a graduation gift.. but back to ur ques, i think MM is a good size for her.. good luck!
150cm is on the shorter side, so GM may look huge on her.
MM is the safer choice. Or even take her to LV to try them on, it would be so exciting for her!