Precompiling regexes can make a dramatic difference. Compare the stats below for u1 vs u5 -- there's an 868% speedup on my box!

Nevertheless, the backreference is just a better algo, and it still wins. 

use Benchmark qw( cmpthese ) ;

my $digits = 2491306578;
my @regexes = map { qr/$_/ } 0 .. 9; 

cmpthese( -5, {
    u1 => sub{
               for ( 0 .. 9 ) { 
                  return 0 if $digits !~ /$_/;
               } 
               return 1;
             },      
        
    u2 => sub{
                my @x = sort split //, $digits;
                my $x = join "", @x; 
                $x =~ tr/0-9//s;
                length $x == 10 ? return 1 : return 0;
              },      
         
    u3 => sub {
                return 0 if $digits =~ /(\d).*\1/; return 1;
              },      
         
    u4 => sub {
                return $digits !~ /(.).*\1/;
              },      
    u5 => sub {
                for (@regexes) { 
                     return 0 if $digits !~ $_; 
                } 
                return 1;
              }

[download]


       Rate    u1    u2    u5    u3    u4
u1  10555/s    --  -71%  -90%  -93%  -93%
u2  35955/s  241%    --  -65%  -76%  -76%
u5 102215/s  868%  184%    --  -32%  -32%
u3 149240/s 1314%  315%   46%    --   -1%
u4 150091/s 1322%  317%   47%    1%    --

[download]
--
Marvin Humphrey
Rectangular Research ― http://www.rectangular.com

In reply to Re^3: Determining uniqueness in a string. by creamygoodness
in thread Determining uniqueness in a string. by Yzzyx

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