I apologize for answering a very old question, but this came in a search of mine and the selected answer is incorrect. Perhaps the chosen answer speaks to the OP's real question, but the question as stated is about
AESCryptoServiceProvider, while the answer is about
RjindaelManaged is an implementation of Rjindael's algorithm that was later selected to become the basis of the AES encryption standard by NIST.
AESCryptoServiceProvider is the best choice for implementing the AES/Rjindael algorithm. AES and Rjindael are both symmetric ciphers.
RSA, the Rivest–Shamir–Adleman cipher system, is an entirely different asymmetric cipher. It is completely unrelated to AES/Rjindael.
The correct answer to when to use
AESCryptoServiceProvider depends on using an asymmetric vs symmetric cipher.
In RSA, you have a public and private key pair. If you want to have a public key to exchange, or if you want your key signed by another party, you want RSA. But RSA is comparatively slow and done properly is one-way: The public key encrypts, the private key decrypts.
If you have a lot of text you want to encrypt, you want AES. It's much faster, and many computers are optimized for it. But there's only one key. Anyone with the key can both encrypt and decrypt, which makes sharing the key safely a priority.
For the best of both worlds, use an RSA public to encrypt and transmit an AES key and then communicate using AES.