The obvious (to me) modest improvement is to change the main loop so that you're only keeping in %master those things that you need to delete from %slave later (since that's all you're doing with it, anyway). For clarity, you should rename %master to %common.

my (%common, %slave);
%slave = map {chomp; $_ => undef} <SLAVE>;

while ( <MASTER> ) {
   chomp;
   if (exists $slave{$_}) { $common{$_} = undef }
   else { print "$_ exists on master but not slave\n" }
}

delete @slave{ keys %common };
print "$_ exists on slave but not master\n" for keys %slave;
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