You can't determine the equality of two values from the equality of their string representations.

To illustrate the point:

$ perl -le '$a = $b = "foo"; print \$a eq \$b ? "true" : "false"'
false
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The strings are identical, but they're two different strings. The string representations of references to them differ. Are they equal or not? This is a question of semantics that you can't answer without additional context.

Indeed, if we just accept the string representation as the universal measure of equality, then ambrus is right: the empty string and undef are equal, and thus all of my arguing has been moot. However, experience tells me it is a prudent bet to assume that in most situations, undef needs to be treated differently from an empty string.

Makeshifts last the longest.

I was thinking of something simpler, such as:

$x = 1.23456;
$y = 1.234560000000001;
print 0+($x == $y); # prints 0 for me
print 0+($x eq $y); # prints 1 for me
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or

$x = 0;
$y = "0";
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Are they equal? Yes and no.