To me it really all boils down to what platform you are comfortable with. 
DNN with MS SQL/ SQL Express and ASP.net framework, or Joomla on MySQL using PHP. 
You can put PHP/MySQL on a Windows box, but I haven't yet heard of anyone getting DNN running on Linux using Mono.

As far as maturity, Joomla(Mambo) has been around longer, and is probably a little more end user friendly, but if you are going to support one or the other, then what I said above seems to be the most important issue.

The core DNN Search has not matured yet, so I wouldn't recommend picking DNN for it's core search, but you may find a third party module with good search capabilities in your specific case.

Joomla is a good platform, no mistake. I have used it for a couple of projects.

The main reason for choosing it over DNN would be the licensing costs of Linux, Apache, MySql and PHP (ie free) v's A Windows Server OS and SQL Server  (a lot if you need to get a SQL Server enterprise license) if the application is to be hosted in house or hosting costs if on a web hosting environment.

Joomla splits out admin much more from the client side application and it is a lot less intuitive than DNN. I would always use DNN given the choice, the development environment for module creation is so much better, and the skinning seems more flexible.

I can't answer your specific search question, unfortunately. Sounds like you'd need a custom module for either platform.