RSA-4096 vs AES-256 for secure chat application? Which of these two methods suits better the implementation of a secure chat application? In this context, chat will be limited up to 150 letters for one message.
I would prefer RSA because what I know RSA is really secure if it is used for small text and also if I will use groups it is easy in RSA because of public key distribution. Specially for chat application where user can write very small letters message I don't know if AES will be good for security.
AES is better in performance specially if I will compare 256 bit vs 4096 bit. RSA will be slower for encrypt and decrypt. But my goal is to have strong secure chat and not super fast chat.
What would be the more apt method?
I will use this chat only for sending message, e.g. no attachments, etc.
RSA and AES do not oppose, and often are rightly used together in hybrid encryption. RSA can do things that AES can not, like allowing encryption to designated recipients, or allowing anyone to check that a message is not altered or from a different person than is apparent. Using AES or other form of symmetric encryption is a must when encrypting more than few hundred characters.

To choose a cryptosystem, you must first define your goals. Secure chat is not nearly precise enough. Confidentiality? Integrity? Proof of origin? Central registry of participants? How is registration and loss of keys handled?