No clue why, but for the future DenverCoder9:

I installed the Apache2 DBD perl module:

perl -MCPAN -e 'install Apache::DBI'

and changed the apache2-perl-startup.pl

use CGI (); CGI->compile(':all');
#use CGI ();
#CGI->compile(':cgi');
use CGI::Carp ();

use Apache::DBI ();
Apache::DBI->connect_on_init('DBI:mysql:otrs;host=loadbalancer', 'otrs', '....');
use DBI ();

and now it is as fast as the old system. I already migrated the old database to the new dedicated mysqlserver but this was not part of the problem (or of the solution).