A test with longer strings shows that the non-greedy regex can be about 25% faster (with perl 5.8.7). My test case regex is designed to match starting near the beginning of the string and ending in the middle.

$ perl -MBenchmark=cmpthese -ne'chomp; $allwords.="/$_"; 
END{
    cmpthese(-3,
       {
         "Greedy"=>sub { 
           $allwords=~m{/abbreviate.+/initial/};
         }, 
         "Nongreedy"=>sub {
           $allwords=~m{/abbreviate.+?/initial/};
         }
       }
    );
}' /usr/dict/words
[download]

The result is:

           Rate    Greedy Nongreedy
Greedy    439/s        --      -22%
Nongreedy 563/s       28%        --

Of course, to repeat this test you'll need /usr/dict/words, and it has to contain abbreviate and initial.

These results are with perl 5.8.7 - I'd be curious to see what happens with 5.8.10, since RE improvements could happen any time.