Hardness Guarantees for AES
As David said, we do not have such reductions for AES. However, this does not mean that Rabin or RSA cryptosystem are more secure than AES. In fact, I'd trust the (at least one-way, probably also pseudorandomess as well) security of block ciphers such as  AES/DES etc.. (perhaps with a bit more rounds than standardly used) more than the assumption that factoring is hard, precisely because there is no algebraic structure and so it's harder to imagine that there will be some kind of breakthrough algorithm.

One can construct block ciphers directly from one-way functions, which is a minimal assumption for much of crpyotgraphy, but the resulting construction will be terribly inefficient and hence not used.