Like in title: which one of these encryption methods (ZipCrypto, AES-256) is more secure and why? I am asking about it because I'd like to know which should be preferred when compressing files with Zip.
According to 7-Zip,

Use ZipCrypto, if you want to get archive compatible with most of the ZIP archivers. AES-256 provides stronger encryption, but now AES-256 is supported only by 7-Zip, WinZip and some other ZIP archivers.

So really there is some balance to be played with. Do you require better security at the sacrifice of compatibility or more compatibility at the sacrifice of security?
According to the Info-Zip FAQ, it sounds like ZipCrypto is pretty weak. Keep that in mind when making your decision.
Note: The link on Info-Zip FAQ to the publication is broken, you can find the file on A Known-Plaintext Attack on the PKZIP Stream Cipher
