compare two tar.bz2

Hello,

I am using a bash script to archive directories of text files located in ${root}:
tar cf ${root}.tar ${root}*
bzip2 ${root}.tar
I'd like to compare the newly produced archive two.tar.bz2 with the second latest one.tar.bz2.
cmp one.tar.bz2 two.tar.bz2
returns
one.tar.bz2 two.tar.bz2 differ: byte 11, line 1
even though I am confident the text files are identical
What would be the right way to compare the archives? I guess they are different because they were produced at two different times?
Thank you
(by the way, comments on the lines used to compress the directories are quite welcome)

why don't you compare size of the files

comparing the sizes of the archives would not work for me because two archives may have the same size but different content. Maybe I should do the work of comparing the files I need to archive before making the archive.