This specific example isn't very good in my opinion since there is only possible matching case per result. However, imagine a situation where you have, say, the numbers 1 till 100, and out of those numbers ie 6, 12, 13, 37, 44, 68 and 99 all need to result in performing some sort of action. Now in a situation like that a switch statement would look something like:

switch($number)
{
  case 6, 12, 13, 37, 44, 68 { \&subroutine(@args); }
  case 1, 29, 77, 98         { \&othersub(@args); }
  default                    { sleep(1); }
}
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whereas if you needed to use if-elsif-else it'd be something like:

if(($number == 6) || ($number == 12) || ($number == 13) || ($number ==
+ 37) || ($number == 44) || ($number == 68))
  { \&subroutine(@args) }
elsif(($number == 1) || ($number == 29) || ($number == 77) || ($number
+ == 98))
  { \&othersub(@args); }
else
  { sleep(1); }
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In this example I actually resorted to copy-pasting $number, having to copy-paste a piece of code over and over again is in itself a sign that what you're doing is inefficient.

Now, the method i personally use atm is to create a hash(or in this example above I'd even have used an array because all the case values are numerical) that would look something like this(copied from actual code I use atm):

my %actions =
  (
  '001'     =>    \&_rpl_welcome,
  '005'     =>    \&_rpl_isupport,
  '332'     =>    \&_rpl_topic,
  '333'     =>    \&_rpl_topicdetails,
  '352'     =>    \&_rpl_whoreply,
  '353'     =>    \&_rpl_namreply,
  'JOIN'    =>    \&_msg_join,
  'PART'    =>    \&_msg_part,
  'KICK'    =>    \&_msg_part,
  'MODE'    =>    \&_msg_mode,
  'QUIT'    =>    \&_msg_quit,
  );

sub process
  {
  my($self, $line) = @_;
  my @text = split(/\s/, $line);
  if($actions{$text[1]})
    { return(&{$actions{$text[1]}}($self, $line, @text)); }
  }
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Long story short, the main argument in favor of a switch-like statement is not having to type $wday for each and every comparison. Repetition = bad :-)