I agree with rach, the smoking slippers are definitely a more trendy silhouette at the moment. I think they're a bit more casual, too, although the distinction is a fine one maybe, and depends as much on fabrication and print as the shape. I would say that the ballet flats are more versatile, and dressier, especially if they are pointy-toe like the ones you have above.
I got a pair of b/w print smoking slippers last fall, and I find I don't wear them much with skirts. They just feel frumpy that way. I think they're nice with jeans and pants. There's the whole high versus low vamp thing, to do with proportions and lengthening the appearance of your leg line. I know Angie's done some posts on this in the past.
I guess the smoking slippers are a tad more masculine, in that they were originally a male garment, not that I see many guys wearing them today. I for sure don't see guys wearing pointy-toed ballet flats, though (unless they're presenting as a woman, of course).