The effectiveness of public key cryptosystems depends on the intractability (computational and theoretical) of certain mathematical problems such as integer factorization. These problems are time consuming to solve, but usually faster than trying all possible keys by brute force. Thus, asymmetric algorithm keys must be longer for equivalent resistance to attack than symmetric algorithm keys.
Для AES сейчас считается достаточным 128 бит, а для RSA минимум 1024. Но вообще это странное сравнение, примерно как сравнивать самосвал и формулу-1