Why don't you try them?

use Benchmark 'timethese';

sub eq_alone    { $_[0] eq 'cr' || $_[0] eq 'CR'; }
sub lc_eq       { lc($_[0]) eq 'cr'; }
sub regex       { $_[0] =~ /^cr$/i; }

timethese (2_000_000, {
        eq_alone => sub { eq_alone('cr'); eq_alone('CR'); },
        lc_eq    => sub { lc_eq('cr');    lc_eq('CR');    },
        regex    => sub { regex('cr');    regex('CR');    },
});

__END__

Benchmark: timing 2000000 iterations of eq_alone, lc_eq, regex...
  eq_alone: 22 secs (21.48 usr  0.00 sys = 21.48 cpu)
     lc_eq: 22 secs (22.76 usr  0.00 sys = 22.76 cpu)
     regex: 25 secs (24.88 usr  0.00 sys = 24.88 cpu)
[download]

In short, using lc is roughly just as expensive as a simple 'eq', giving us the same results as doing a double 'eq'. Using a regex adds only a few seconds.

In many cases like this (where the numbers are so close), performance matters less than readability. Use whatever is easier for you to comprehend and easiest for future maintainers to read. I usually vote for using lc in cases like this.