A quick change to your benchmark measures more accurately what we are talking about. Assume the evals and string qoutes are right because you lost me in there somewhere.

use strict;
use warnings;
 
use Benchmark("cmpthese");
  
cmpthese(-1, {
  'double'     , q !eval q {$a = "this is a string \$i"}!,
  'single'     , q !eval q {$b = 'this is a string $i'}!,
  'double no $', q !eval q {$a = "this is a string"}!,
  'single no $', q !eval q {$b = 'this is a string'}!,  
});


__DATA__

C:\test>perl interpolation_bench.pl
               Rate      double      single double no $ single no $
double      22226/s          --        -16%        -17%        -17%
single      26331/s         18%          --         -2%         -2%
double no $ 26733/s         20%          2%          --          0%
single no $ 26733/s         20%          2%          0%          --

C:\test>perl interpolation_bench.pl
               Rate      double      single double no $ single no $
double      21065/s          --        -20%        -21%        -21%
single      26331/s         25%          --         -1%         -2%
double no $ 26714/s         27%          1%          --         -0%
single no $ 26756/s         27%          2%          0%          --

C:\test>perl interpolation_bench.pl
               Rate      double      single single no $ double no $
double      21966/s          --        -17%        -18%        -18%
single      26551/s         21%          --         -1%         -1%
single no $ 26733/s         22%          1%          --         -1%
double no $ 26947/s         23%          1%          1%          --

C:\test>perl interpolation_bench.pl
               Rate      double      single single no $ double no $
double      22226/s          --        -14%        -16%        -17%
single      25960/s         17%          --         -1%         -3%
single no $ 26331/s         18%          1%          --         -2%
double no $ 26733/s         20%          3%          2%          --

C:\test>perl interpolation_bench.pl
               Rate      double double no $      single single no $
double      20785/s          --        -19%        -21%        -23%
double no $ 25551/s         23%          --         -3%         -5%
single      26211/s         26%          3%          --         -3%
single no $ 27019/s         30%          6%          3%          --
[download]

You see a consistent win for single quotes, I don't think it is enough to worry about though. If you are dealing with 100k strings and you want to decide if you should sinle or double quote them, then you probably made a bad choice to load 100k variables ;)

Update: Added benchmarks for strings with no $ in them. Looks like perl must do a prescan to see if it needs work or not. I could of course be completely crazy.