Well, they do have different goals. Rivets wants to be a small plugin that works with any framework while knockout is also designed to bring structure to the party.
For me it's like comparing an engine with a car.
One big upside to knockout is that the lib is a little under 3KB minified while knockout is 40KB minified.
I prefer having smaller libraries that are really good at what they do.
What "structure" are we talking about with KO? I've been using it for a couple weeks just to do binding, and I haven't noticed it introducing any particular structure to my applications.
It is nothing like Backbone, which really seems to want you to write a "Backbone" app.
One big upside to knockout is that the lib is a little under 3KB minified while knockout is 40KB minified.
I prefer having smaller libraries that are really good at what they do.