I think Abigail-II is right:

Benchmark: timing 1000000 iterations of method1, method2, method3...
   method1: 71 wallclock secs (69.22 usr +  0.13 sys = 69.35 CPU) @ 14
+419.61/s (n=1000000)
   method2: 39 wallclock secs (39.21 usr +  0.00 sys = 39.21 CPU) @ 25
+503.70/s (n=1000000)
   method3: 100 wallclock secs (96.76 usr +  0.13 sys = 96.89 CPU) @ 1
+0320.98/s (n=1000000)
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• method1 uses the regex-engine to loop and count the matches. The engine isn't cheap to use, but faster than method3, that builds this loop in perl.
• method2 is fastest, because searching a fixed string using index without the overhead (in this case) of the regexp-engine is faster, as Abigail-II explained.
• method3 is slowest, because it uses the regexp-engine as does method1, but builds the loop-construct to count matches within perl-code, requiring more overhead in perl to manage the loop

The Benchmark-code:

#!/usr/bin/perl
 use strict;
 use warnings;
 use Benchmark;

my @test = ("a a a a","a a a", "a a", "a", "a a a a","a a a", "a a", "
+a","a a a a","a a a", "a a", "a");

 sub method1 {
 my $text=shift;
 my $gene=shift;
 my $count = () = $text =~ /$gene/g;

 return $count;
 }

 sub method2 {
 my $text=shift;
 my $gene=shift;
 my $count=0;

 my $p=0;
 ++$count while $p = 1+index( $text, $gene, $p );

 return $count;
 }

 sub method3 {
 my $text=shift;
 my $gene=shift;
 my $count=0;

 my $patn = qr/\b$gene\b/;
 $count++ while $text =~ /$patn/g;

 return $count
 }
timethese(1000000, {
   method1 => sub { foreach (@test) {method1($_,'a')}},
   method2 => sub { foreach (@test) {method2($_,'a')}},
   method3 => sub { foreach (@test) {method3($_,'a')}},
   }
   );
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regards,
tomte

edit:: added interpretation of results

Hlade's Law:

If you have a difficult task, give it to a lazy person --
they will find an easier way to do it.