Well, is it more popular because that is just what people are used to downloading or the first download link on the web page? Or is it because people fundamentally prefer tgz files over tar.bz2?
These questions are difficult to answer with the download stats alone. If you really want to know, we should setup a poll...
Are there actual platforms that can't handle tar.bz2 but can handle tgz?
That, in turn, is easy to answer: yes, there are. Certain Solaris releases had gzip available (even though /usr/bin/tar wouldn't know how to invoke it), but no bzip2 utility.
I'm willing to bet it's because of the download link order and has nothing to do with actual preference (especially since we don't state file size on the download page).
Not sure what page you are looking at; on
Personally I don't know why we have both tgz and tar.bz2 other than tradition. I say trim it down to tar.bz2 for portability and move on to using a ustar-based tar.xz to be cutting edge and minimize download size overall while making it the first download option to make sure people notice it. I'd also vote for listing the file size on the download page, but that's just another step for release managers that I don't want to burden them with.
You would also need to specify what page you refer to as "the download page".