Packing a bunch of files together as .tgz is a quite universal format and compresses most of the redundancy out. It has some pathological cases but those are rare, and for general files it's still in the same ballpark with other compressors.

I remember using .tbz2 in the turn of the millennium because at the time download/upload times did matter and in some cases it was actually faster to compress with bzip2 and then send over less data.

But DSL broadband pretty much made it not matter any longer: transfers were fast enough that I don't think I've specifically downloaded or specifically created a .tbz2 archive for years. Good old .tgz is more than enough. Files are usually copied in seconds instead of minutes, and really big files still take hours and hours.

None of the compressors really turn a 15-minute download into a 5-minute download consistently. And the download is likely to be fast enough anyway. Disk space is cheap enough that you haven't needed the best compression methods for ages in order to stuff as much data on portable or backup media.

Ditto for p7zip. It has more features and compresses faster and better but for all practical purposes zip is just as good. Eventhough it's slower it won't take more than a breeze to create and transfer, and it unzips virtually everywhere.