Can I say that 128 bit using AES provide more security than 1024 using RSA?
They're not really directly comparable. The number commonly bandied about is 2048-bit RSA is about equivalent to 128-bit AES. But that number shouldn't be relied on without understanding the caveats.
Currently the most effective way of breaking AES crypto (and any other unbroken symmetric cipher, for that matter) is brute-force. You simply try every possibility until you reach the correct result.
This means that it is possible, and well within today's technology, to encrypt data that (assuming no better attack is ever found--not a horrible assumption), can never be broken, ever, by anyone. Simply use enough bits in your key such that there isn't enough energy in the universe to try enough candidate keys. The numbers are smaller than you'd think:
Indeed, with AES, 128-bit is secure against modern technology, 256 is secure against any likely future technology, and 512 is probably secure against even never-imagined hypothetical alien technology.
Symmetric encryption, if not broken, doesn't leave you with a math problem to solve. The numbers are truly and literally scrambled, and the system is devised such the brute-force is by far the most efficient solution.
Breaking RSA, on the other hand, is not so hard. Instead of brute-forcing the keys, you factor the modulus into primes and derive the keys yourself. This is dramatically simpler to do. It's a math problem, and we can do math.
Specifically, the speed at which primes can be factored is increasing FASTER than the speed at which symmetric keys can be brute-forced. And that's with today's technology.
But going forward, assuming quantum computers can be improved such that qbit operations are a cheap as bit operations (which many people thinks is fairly close; this century at most, possibly decades), then no matter how large you make your RSA key, breaking the key is as fast as encrypting.
So the moral of the story is this:
The "equivalent security" of RSA key length versus AES key length changes over time. Every so often, you have to increase your RSA key size relative to your AES key size to account for technological advances. And even then, it's an estimate at best.
And while a 256-bit symmetric key should be secure for hundreds, thousands, or perhaps hundreds of thousands of years, no RSA key of any length should be assumed to be secure more than a few dozen years out, since RSA is expected to be completely and utterly broken by Shor's algorithm.
Any commonly used symmetric encryption algorithm (DES,3DES, AES,...) is normally faster than RSA.
From a similar question on stack overflow:
Also have a look at this paper: http://ijsr.net/archive/v2i4/IJSRON120134.pdf The following graph on performance was taken from it:
The effective security provided by AES-128 is approximately 126-bits due to some reduced rounds attacks on AES. That is, it lost a couple of bits of theoretical security.
The effective security provided by 1024-RSA is 80-bits. Breaking RSA reduces to factoring RSA or discrete logs in finite fields. The best method is the number field sieve (NFS).
126-bits of security is stronger/greater than 80-bits of security.
Effective security levels are moving target. As cryptanalysis advances, so will the loss in theoretical security. An example of a considerable loss is SHA-1. SHA-1 provides 80-bits of theoretical security due to collisions and birthday attacks. But due to Marc Stevens' 2011 HashClash attack, SHA-1 has about 61-bits of effective security.
61-bits of security is not enough to maintain security over digital certificates that require long-surviving signatures because a workload of 261 is within reach of many attackers.
Oddly, Mozilla's is Phasing out Certificates with 1024-bit RSA Keys blog. So they are risk adverse to 80-bits of security on long lived CA certificates. But SHA-1, with 61-bits of security, is OK. You do the math....
More generally, there are tables of equivalent security levels available. You can find the NIST tables below. Other organizations that publish the criteria include NESSIE, ECRYPT, ISO/IEC.