Two comments from my side. First, your subroutine does the same thing twice. I would change it such that it reads the filtered contents of a given file into a given array and call it twice. Second, your while loop is essential equivalent to grep, so in summary, I would rewrite your code as:

my @seq1 = load_seqs( "q1.fa" );
my @seq2 = load_seqs( "q2.fa" );

sub load_seqs{
    open my $fh, "<", shift or die "cannot open sequence file: $!";
    return grep { /^(?!\>).*\n$/ } <$fh>;
}
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