Good code.

However, you said that you knew no way to "tell Text::Diff to ignore trailing blanks as being insignificant." I decided to explore this and found that the following code works:

#!/usr/bin/env perl

die "Usage: $0 from-file to-file\n"
  unless @ARGV == 2;

use Text::Diff;

diff shift, shift,
  { OUTPUT => \*STDOUT,
    STYLE => "OldStyle",  # or whatever pleases you
    KEYGEN => sub{ (my $line = shift) =~ s/\s*$//; return $line; },
  };
[download]

In general, to compare something other than the lines themselves, just return that from the KEYGEN argument. For example, inserting sub{return substr shift, 0, 1} compares only the first characters. Unfortunately, the documentation for this is hidden in Algorithm::Diff.