I benchmarked this and it yields an interesting result. index() is (a bit) faster than a regex. If itīs used in combination with lc(), as in your example, the regex with the i-modifier is faster.

use strict;
use warnings;

use Benchmark;

my $value = "somewhere here true is there!";

timethese
(
    9000000,
    {
            'index' => sub { index( $value, "true" ) },
            'regex' => sub { $value =~ /true/ },
    }
);

timethese
(
    9000000,
    {
            'index' => sub { index( lc $value, "true" ) },
            'regex' => sub { $value =~ /true/i },
    }
);


Benchmark: timing 9000000 iterations of index, regex...
     index:  2 wallclock secs ( 2.02 usr +  0.00 sys =  2.02 CPU) @ 44
+46640.32/s (n=9000000)
     regex:  4 wallclock secs ( 2.40 usr + -0.01 sys =  2.39 CPU) @ 37
+60969.49/s (n=9000000)
Benchmark: timing 9000000 iterations of index, regex...
     index:  4 wallclock secs ( 4.55 usr +  0.00 sys =  4.55 CPU) @ 19
+79762.43/s (n=9000000)
     regex:  3 wallclock secs ( 3.68 usr +  0.00 sys =  3.68 CPU) @ 24
+48313.38/s (n=9000000)
[download]

Update:
Ack. I really need to learn to type faster.