Here's the start of another approach, based on using Algorithm::Diff to count the number of common words (in sequence) between two arrays of strings. By computing a percentage based on the smaller of the arrays, you address both the case of the submitted quote being a subset of an existing quote, and vice versa.

Here's how it hands the "gonna" -> "going to" change.

use strict;
use Algorithm::Diff qw(traverse_sequences);

my @quote1 = split(' ', <<QUOTE);
I walk. I talk. I shop, I sneeze. 
I'm gonna be a fireman when the floods roll back.
There's trees in the desert since you moved out. 
And I don't sleep on a bed of bones.
QUOTE

my @quote2 = split(' ', <<QUOTE);
I'm going to be a fireman when the floods roll back.
There's trees in the desert since you moved out.
QUOTE

my $match = 0;
traverse_sequences(\@quote1, \@quote2,
                    { MATCH => sub { $match++ } }
                  );

my $smaller = @quote1 < @quote2 ? @quote1 : @quote2;
my $percent_match = int(($match / $smaller) * 100);

print "$match words matched ($percent_match%)\n";
__END__
18 words matched (90%)
[download]

To make this work in practice, you would need to do things like ensure that the shorter quote was at least n words long, so that a 1 word candidate quote didn't match at 100%.

A few minutes perusing the Algorithm::Diff POD might give you some additional ideas.