Simple Summary:-

Gzip Pros:-
>> Low Compression Time
>> Low Decompression Time
>> Gzip is compatible with most browsers since 2000

>> Very poor Compression Size
>> Very slow Compression Speed
>> Very slow Decompression Speed

Bzip2 Pros:-
>> Bz2 is compatible mostly for FastDL/Redirects FTPs for SRCDS servers
>> Very fast Decompression Speed

>> Very high Decompression Time
>> Compression rate isn't significantly improved compared to gzip

Xz Pros:-
>> Xz compresses zips approximately 34% more than gzip
>> Fast Decompression Speed
>> Xz is compatible when a Tarball archive .tar file is compressed as a tar.xz Linux zip archive.

>> Very high Compression Time when XZ compression is set at a higher Compression Level.