So you are trying to find differences that might explain the behavior?
If you reduce it to case of calling the file a.tar, from the users home directory, creating a directory call blah, and running cd blah; ../tar -xvf ../a.tar on both boxes does it reproduce the issue. This will eliminate variables... always a good thing in issue isolaton.
AIX is a complex environment and that one difference might require almost an army of information:
Things to check
cksum ksh see if they are the same... if they are not copy the working one to the broken machine and see if it resolves it... this has happened to me several times
output from strace and ltrace on your tar operatoin... You can glean some hints as to what tar was up to when it decided to die
ldd on tar and cksum all of its dependent libraries
truss or tusc (warning may be HP I work on a lot of boxes)
Goto Page 488 on this for some settings with serious implications if they are different.
Suggestion 5 is a wealth of information on AIX.