Well, my first thought was simply to write something that was simple, and not to worry about the speed. It depends on how many tens of million times this is going to happen before the speed even becomes an issue.

However, since you asked:

use Benchmark;
$a="Hello";
timethese(10_000_000, { eq => sub { return ($a eq "" || $a eq "?") },
                         regexp => sub { $a=~/^\??$/ } } );
[download]

gives

Benchmark: timing 10000000 iterations of eq, regexp...
        eq:  7 wallclock secs ( 3.51 usr + -0.01 sys =  3.50 CPU) @ 28
+57142.86/s (n=10000000)
    regexp: 22 wallclock secs (10.15 usr +  0.13 sys = 10.28 CPU) @ 97
+2762.65/s (n=10000000)
[download]

The figures don't change (significantly) when $a="?". When it's an empty string, the equality takes half the time (since the second equality is never used), and the regexp is slightly slower (because it has to backtrack). undef makes both slightly slower.

--
Tommy
Too stupid to live.
Too stubborn to die.