That's an awfully tough question to answer accurately without really doing an in depth analysis of your app and your requirements.
On the surface, there is no reason why two apps couldn't share the same database.
The devil is in the details though.
Concurrency issues, sessions....
While it might be fun to start a .NET vs
J2ee flame war, I doubt you'll really get any information that you can use from a forum (from either camp) in this case.
If you're app is strictly a hosted model, then you probably won't care much about platform independence so the vendor lock-in from going to .NET probably won't matter. On the other hand, if it's written in Perl, it's most likely already sitting on an *nix system.
Bottom line is, you've got a lot to consider and nobody on a forum is going to be able to help you much with it.