Why do you open file2 for every key in %hash1, go through that file from start to end to only look at the key at one line?

It suffices to open file2 once, read in key/value pairs (as you did with file1); whilst doing so you can find out whether the current key exists in file1:

    open TWO, '<', $FILE2;        # better be explicit ;-)
    while (<TWO>)
    {
        chomp;                    # correct indent level is here.
        my ($key,$value) = split /\s+/,$_;
        print "$key NOT IN FILE 1\n" unless $hash1{$key};
        $hash2{$key} = $value;
    }
[download]

foreach my $key (keys %hash1)
{
    if(exists($hash2{$key})
    {
        if($hash1{$key} == $hash2{$key})    # '==' if numeric, 'eq' if
+ string
        {
            ...
        }
        else 
        {
            ...
        }
    }
    else    # this is the case you missed - $key not in file2
    {
        ...
    }
}
[download]

--shmem

_($_=" "x(1<<5)."?\n".q·/)Oo.  G°\        /
                              /\_¯/(q    /
----------------------------  \__(m.====·.(_("always off the crowd"))."·
");sub _{s./.($e="'Itrs `mnsgdq Gdbj O`qkdq")=~y/"-y/#-z/;$e.e && print}