Some oneliners that hopefully will give you some hints
Better development environment
The development environment is pretty mature and with lot of features.
Although not radically different than VS 6 it has lots of improvements.
Webservices
You can create and consume webservices with ease. This way you can
provide cross-platform compatible communication with your application.
Enterprise Serviced Components
You can leverage the power of the provided services and build
enterprise scalable applications easily.
Cleaner Development Model
Personally, I think that C# and OO provides a simpler and more robust
development model.
ADO.NET
A managed framework for accessing data. It's mostly data-source
agnostic, so it gives you a great deal of flexibility.
Support and compatibility issues
By developing an application (especially a big one) in VB6, you invest
in a technology that it's old. I don't know Microsoft plans about VB
support
Easier Installation
You have no DLL hell and you can deploy an application simply by XCopy.
Mono
There is an OpenSource implementation of the .Net framework that you
can use to develop cross-platform applications.
Fashion
Although it may sound funny lots of bosses like trendy technologies.