Just speaking for how it works in Seattle, buy nothing groups are often more about making hyper local connections with neighbors and not quite so focused on the efficient transfer of goods. For example as soon as one gets too big, they split it up into smaller groups. It diminishes the audience for your post. I've also observed some odd behaviors in the buy nothing groups on Facebook I've been on where it seems like people are putting way too much effort into a posting for one single t-shirt or dress with elaborate descriptions. It seems like there's something going on that's not just about getting rid of stuff.

Freecycle on the other hand has broader distribution in one sense in that they don't force you to limit your audience. And no reliance on Facebook.