RoboSpice(RS) is service based and more respectful of Android philosophy than Volley. Volley is thread based and this is not the way background processing should take place on Android. Ultimately, you can dig down both libs and find that they are quite similar, but our way to do background processing is more Android oriented, it allow us, for instance, to tell users that RS is actually doing something in background, which would be hard for volley (actually it doesn't at all).
RoboSpice and volley both offer nice features like prioritization, retry policies, request cancellation. But RS offers more : a more advanced caching and that's a big one, with cache management, request aggregation, more features like repluging to a pending request, dealing with cache expiry without relying on server headers, etc.
RoboSpice does more outside of UI Thread : volley will deserialize your POJOs on the main thread, which is horrible to my mind. With RS your app will be more responsive.
In terms of speed, we definitely need metrics. RS has gotten super fast now, but still we don't have figure to put here. Volley should theoretically be a bit faster, but RS is now massively parallel... who knows ?
RoboSpice offers a large compatibility range with extensions. You can use it with okhttp, retrofit, ormlite (beta), jackson, jackson2, gson, xml serializer, google http client, spring android... Quite a lot. Volley can be used with ok http and uses gson. that's it.
Volley offers more UI sugar that RS. Volley provides NetworkImageView, RS does provide a spicelist adapter. In terms of feature it's not so far, but I believe Volley is more advanced on this topic.
More than 200 bugs have been solved in RoboSpice since its initial release. It's pretty robust and used heavily in production. Volley is less mature but its user base should be growing fast (Google effect).
RoboSpice is available on maven central. Volley is hard to find ;)