It's certainly easier to point out their differences, as the two characters are radically dissimilar. However, I would say that one trait the two women definitely share is their ability to extract themselves from situtations. Lulu leaves crazy Moses after the birth of Gerry. Marie cooks up the elaborate story about the marks of the cross appearing on her hand after she's stabbed by a fork. The story lets her escape the convent.
While both of these characters are able to escape, their freedom is only temporary. Lulu winds up in a burned out shack and at the mercy of the government. Marie is freed from the convent, only to be raped by Nector, married and then seemingly perpetually pregnant.
The fate of the Marie and Lulu is in many ways analogous to the fates of Native Americans who find that despite their intelligence and abilities, they are nonetheless trapped in a hopeless situation.