You need \Q...\E which quotes metacharacters in regexes.

if ($a =~ m/\Q$b\E/)
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See also quotemeta

By the way, $a and $b have a special meaning to Perl (because of their use in sorting) so it's a really bad idea to use them for anything else.

Your suspicions are correct. The + is a special character in regexps. You need to escape it. Here are two methods of doing it programatically:

if ($a =~ m/\Q$b\E/i)
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$b = quotemeta($b);
if ($a =~ m/$b/i)
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References: perlre and quotemeta

Update: It's much faster to use string functions when dealing which constant strings. Case-insensitivity is obtained by converting both strings to a common case using lc or uc.

if (lc($a) eq lc($b))
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It's the use of eq instead of m// that makes it work, not the conversion to lowercase. Converting to lowercase is to string compares what /i is to regexps.

#!/usr/bin/perl

use strict;
use warnings;

$a = "I have to get the + version";
$b = "I have to get the + version";

# if($a =~ m/$b/i)
if (lc($a) eq lc($b))
{
    print "Ok\n";
}
else
{
    print "Not the same...\n";
}
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