Write subs not comments, write

 
my @dbs = (
    [ 'OWNER', 'dbi:...', 'user', 'pass' ],
    [ 'OWNER', 'dbi:...', 'user', 'pass' ],
);
for my $db( @dbs ){
    LogStats( @$db );
}
...
sub LogStats {
     my( $filename, $dsn, $user, $pass ) = @_;
     ...
     my $dbh = DBI->connect( $dsn, $user, $pass, {qw/RaiseError 1/} );
     open my($fh), ...
##   QueryOne( $dbh, $fh, ... );
     CreateTableStats( $dbh, $fh, ... );
     PopulateTableStats( $dbh, $fh, ... );
     DumpTableStats( $dbh, $fh, ... );
}
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Note the RaiseError, saves you from writing "or die" all over

Then if there is a problem in Query4 on line 151 you can debug it independently from rest of the program

Closing the statement handle inside this loop is your mistake

If you write this way you don't need to explicitly close it

sub Query4Over500 {
    my ( $dbh, $FHExtract, $tb_name ) = @_;
    $tb_name = $dbh->quote_identifier( $tb_name );
    my $sql = "select * from $tb_name";
    my $sth =  $dbh->prepare( $sql );
    $sth->execute;
    while (my $aref = $sth->fetchrow_arrayref) {
        print $FHExtract ToCsv( $aref );
    }
}
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