One difference, according to warn, occurs if you have a __WARN__ handler:

No message is printed if there is a $SIG{__WARN__} handler installed.

Update: another subtle difference is that you get line info if you leave off the newline in warn (not sure why):

use strict;
use warnings;

print STDERR "print\n";
warn "warn with newline\n";
warn "warn without newline";

__END__

print
warn with newline
warn without newline at z line 11.
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