The first two replies above (Elian and sauoq) are fine for the situation where you may be handling multiple references to the same instance of an object. But there may also be the case where two independent data structures (two separate instances of the same type of object) are created and populated, and happen to end up containing identical data values. Just comparing the object handles won't detect this sort of identity.
I wonder whether Data::Dumper might provide a useful shortcut in this case (I haven't had occasion to use it myself yet) -- if nothing else, you may be able pass the Dumper's output for each object to Digest::MD5, and see whether the two objects have identical signatures.
update: Having just read the first paragraph of the OP more carefully, I realize that I missed the point and my remarks are not relevant (interesting, maybe, but not relevant). Elian and sauoq are right -- whoever wrote the original code was simply checking to see whether $obj1 and $obj2 were both references to the same instance of an object.
(one more update: since you're trying to scope out someone else's complicated, multi-file perl code, I could put in a plug for a tool I posted here to tabulate subroutines in multiple related perl files (calls and definitions). Hope it helps.