Zip has terrible compression ratio compared to modern formats, it's also a mess of different partially incompatible implementations by different software, and also doesn't enforce utf8 or any standard for that matter for filenames, leading to garbled names when extracting old files. Its encryption is vulnerable to a known-plaintext attack and its key-derivation function is very easy to brute force.
Rar is proprietary. That alone is reason enough not to use it. It's also very slow.