the Damier looks more grown-up and professional; bags like the Sac Plat, Speedy, Alma and the messenger bags look better in the Damier line. and a big plus is that they're all vachetta-less, and therefore worry-free.
the Monogram is more casual, but there are some bags that will look good only in that line, like the Manhattan, Batignolles and Popincourt bags.
so it really does depend on the bag.