All these posts have used regexes that are too simple. Here's my benchmark (on 5.8.3):

use Benchmark 'cmpthese';

my $y = "HELLO world" x 100;

cmpthese(-5, {
  cc_simple => sub {
    $y =~ /[hH][eE][lL][lL][oO]/;
  },
  cc_complex => sub {
    $y =~ /\w+ [hH][eE][lL][lL][oO] \w+/;
  },
  i_simple => sub {
    $y =~ /hello/i;
  },
  i_complex => sub {
    $y =~ /\w+ hello \w+/i;
  },
  simple => sub {
    $y =~ /HELLO/;
  },
  complex => sub {
    $y =~ /\w+ HELLO \w+/;
  },
  simple_fail => sub {
    $y =~ /hELLO/;
  },
  complex_fail => sub {
    $y =~ /\w+ hELLO \w+/;
  },
});

__END__
                  Rate cc_complex i_complex complex complex_fail simpl
+e_fail cc_simple i_simple simple
cc_complex     13973/s         --       -2%    -82%         -83%      
+  -87%      -99%     -99%   -99%
i_complex      14271/s         2%        --    -81%         -83%      
+  -87%      -99%     -99%   -99%
complex        77103/s       452%      440%      --          -7%      
+  -31%      -93%     -93%   -94%
complex_fail   82560/s       491%      479%      7%           --      
+  -26%      -92%     -93%   -94%
simple_fail   111335/s       697%      680%     44%          35%      
+    --      -90%     -90%   -92%
cc_simple    1065985/s      7529%     7370%   1283%        1191%      
+  857%        --      -5%   -23%
i_simple     1120558/s      7919%     7752%   1353%        1257%      
+  906%        5%       --   -19%
simple       1377591/s      9759%     9553%   1687%        1569%      
+ 1137%       29%      23%     --
[download]

You can see that, for the very simple regex, the /i regex is faster than the charclass regex -- but this is because, even with case-sensitivity on, the regex /hello/ is a simple Boyer-Moore search (compare "simple" and "i_simple"). Once you get into a complex regex -- one that requires actual pattern matching -- you can see that /i and charclasses operate about the same (compare "cc_complex" and "i_complex").