Ok, I ran the benchmark, and it seems the regex form is faster. I have tested it several times with the following code and results:

use Parse::RecDescent;
use Date::Calc qw(:all);
use Benchmark ':all';
use strict;
use warnings;

my $grammar1 = q~

   logic: expression eod
      { $return = $item[1]; }

   expression: <leftop: term termop term>

   termop: /and/i | /xor/i | /or/i

   term: '(' <commit> expression ')'
      { $return = $item[3]; } #[@item[1,3,4]]; }  # Only include eleme
+nts important to later processing
       | condition


   condition: element comparison element
      {
         $return = main::process(@item[1..3]);
      }

   element: '<' <commit> /-?\w+/ '>'
      {   $return = "<$item[3]>"; }  #Return this so that the conditio
+n value can be set
          | /\d+/                    # num is automatically returned

   comparison: /(=[><]=)/ <commit> <error: Unable to match comparison,
+ $1>
             | /=?[><]=?/
             | '='
             | '!='

   eod: /^\Z/

~;

my $grammar2 = q~

   logic: expression eod
      { $return = $item[1]; }

   expression: <leftop: term termop term>

   termop: /and/i | /xor/i | /or/i

   term: '(' <commit> expression ')'
      { $return = $item[3]; } #[@item[1,3,4]]; }  # Only include eleme
+nts important to later processing
       | condition


   condition: element comparison element
      {
         $return = main::process(@item[1..3]);
      }

   element: '<' <commit> /-?\w+/ '>'
      {   $return = "<$item[3]>"; }  #Return this so that the conditio
+n value can be set
          | /\d+/                    # num is automatically returned

   comparison: '<=' | '<' | '=' | '>=' | '>' | '!='

   eod: /^\Z/

~;

my $parser1 = new Parse::RecDescent($grammar1) or die;
my $parser2 = new Parse::RecDescent($grammar2) or die;

my $test = '<DAY> = 4 or <DAY> > 4 or <DAY> < 4 or <DAY> >= 4 or <DAY>
+ <= 4 or <DAY> != 4';

cmpthese(10000,{
   'regex' => sub { $parser1->logic($test); },
   'quote' => sub { $parser2->logic($test); },
   });
[download]

---

Yielded:

       Rate quote regex
quote 116/s    --   -5%
regex 123/s    6%    --
[download]

---

This one added the =>= which I wanted to avoid, and while it slowed down both slightly, the regex was still in the lead.

use Parse::RecDescent;
use Date::Calc qw(:all);
use Benchmark ':all';
use strict;
use warnings;

my $grammar1 = q~

   logic: expression eod
      { $return = $item[1]; }

   expression: <leftop: term termop term>

   termop: /and/i | /xor/i | /or/i

   term: '(' <commit> expression ')'
      { $return = $item[3]; } #[@item[1,3,4]]; }  # Only include eleme
+nts important to later processing
       | condition


   condition: element comparison element
      {
         $return = main::process(@item[1..3]);
      }

   element: '<' <commit> /-?\w+/ '>'
      {   $return = "<$item[3]>"; }  #Return this so that the conditio
+n value can be set
          | /\d+/                    # num is automatically returned

   comparison: /(=[><]=)/ <commit> <error: Unable to match comparison,
+ $1>
             | /=?[><]=?/
             | '='
             | '!='

   eod: /^\Z/

~;

my $grammar2 = q~

   logic: expression eod
      { $return = $item[1]; }

   expression: <leftop: term termop term>

   termop: /and/i | /xor/i | /or/i

   term: '(' <commit> expression ')'
      { $return = $item[3]; } #[@item[1,3,4]]; }  # Only include eleme
+nts important to later processing
       | condition


   condition: element comparison element
      {
         $return = main::process(@item[1..3]);
      }

   element: '<' <commit> /-?\w+/ '>'
      {   $return = "<$item[3]>"; }  #Return this so that the conditio
+n value can be set
          | /\d+/                    # num is automatically returned

   comparison: '<=' | '<' | '=' | '>=' | '>' | '!='

   eod: /^\Z/

~;

my $parser1 = new Parse::RecDescent($grammar1) or die;
my $parser2 = new Parse::RecDescent($grammar2) or die;

my $test = '<DAY> = 4 or <DAY> > 4 or <DAY> < 4 or <DAY> >= 4 or <DAY>
+ <= 4 or <DAY> != 4 or <DAY> =<= 4';

cmpthese(10000,{
   'regex' => sub { $parser1->logic($test); },
   'quote' => sub { $parser2->logic($test); },
   });
[download]

---

Yielded:

       Rate quote regex
quote 104/s    --   -7%
regex 113/s    8%    --
[download]

---

I admit, neither is as fast as I would like, but it certainly appears that the regex is the fastest method there, unless I made a mistake.

Edit: If you feel this was biased in any way, feel free to suggest another string, or another test altogether. I don't use the benchmark module frequently, and I may have inadevertently allowed for some bias.

---

My code doesn't have bugs, it just develops random features.

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