I would think that ASP.NET using VB.NET code-behind would be an easier transition then VB to ASP. First of all, you have an intuitive UI designer that is not all that different from creating VB forms. Second, the business logic code is nicely separated from the UI, unlike classic ASP which is an untidy mix of UI and business logic code. Third, ASP.NET has built in ways of maintaining the state of controls, where as in ASP you have to write extra code to refill the controls everytime the page is posted back.
VB.NET has some differences to VB6, but then the VBScript you would use in ASP is also a little different then VB.