On the up side:
You have a more modern tool with latest windows controls.
Better GUI
All .NET languages (vb/c# etc.) are compatible with each other, can be used interchangebly in most situations and can also be converted easily from one language to another, since they compile to a common base language (MSIL) and use the same runtime (CLR).

On the downside:
The .NET runtime is huge as compared to the VB6 runtime which was just a few MB.
Your programs will not run without the .NET runtime.
Code does not compile to native executables, but instead compile to an intermediate language (called MSIL) and is compiled at runtime by the framework. This is usually a boon, but bad as far as code secrecy/decompilation is concerned (though we have options to make it harder).