same query, two different approaches, vastly different performance

I asked this on Stackoverflow and on Perlmonks, but hopefully I will get a more satisfactory and revealing insight straight from the DBI folks.

I have a Postgres table with more than 8 million rows. Given the following two ways of doing the same query, I get wildly different results.

	$q .= '%';

	## query 1
	my $sql = qq{
    		SELECT a, b, c
    		FROM t 
    		WHERE Lower( a ) LIKE '$q'
	};
	my $sth1 = $dbh->prepare($sql);
	$sth1->execute();

	## query 2
	my $sth2 = $dbh->prepare(qq{
    		SELECT a, b, c
    		FROM t  
    		WHERE Lower( a ) LIKE ?
	});
	$sth2->execute($q);


query 2 is at least an order of magnitude slower than query 1... seems like it is not using the indexes, while query 1 is using the index. And, yes, I have tried it with query 2 before query 1 to eliminate caching. There is a difference, but I don't know why, so would love hear an explanation.

Many tia,


--
Puneet Kishor