RSA-4096 vs AES-256 for secure chat application?
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?