The problem is that the widely-deployed AES ciphersuite, like the ciphersuites for triple DES and IDEA, uses a construction from the '90s that is itself insecure. It's based on CBC mode (which is fine) in a MAC-then-encrypt configuration (which is not), which lead to the Lucky 13 attack, and which until TLS 1.1 didn't properly set up the IVs for each record, which lead to BEAST.
No major site used RC4 because it was more performant. They used it as a workaround to Lucky 13 and BEAST, because they couldn't count on browsers fixing those problems fast enough.