I think you mean the Dior New Lock Promenade pouch. The Miss Dior bag currently doesn't come in a pouch with a detachable strap.
Here are some comparison pictures.
I like the lock on the Dior New Lock; it really gives the bag some character. As well, the Dior is bigger and can hold a bit more.
The Chanel is nice, and I love the chain strap. Holds less than the Dior, though.
I can't really decide between the two, so I suggest that you try both of them on at the boutique, and also see if they are large enough to carry your essentials.