What kind of redirect is 123 reg doing?
If it's a frames-based one then anything is better.
Parking the domain properly and using mod_rewrite to redirect it allows all traffic to be presented with the same final destination domain, rather than having multiple 'versions'. It also means that you don't get penalised by search engines for duplicate content, nor do you suffer having PR split across those domains.
To use mod_rewrite:
RewriteEngine On
RewriteCond %{HTTP_HOST} ^(.*)seconddomain\.com
RewriteRule ^(.*) http://www.maindomain.com/$1 [R=301,L]
The domain names would be changed and that then entered into your htaccess file in the root of your site.