Visual Web part
Allows you to Drag and Drop the controls from the Toolbox to Web Part Design surface. You can of course write your custom code in the code file. You can also package and deploy your web parts directly to SharePoint from VS by pressing Clt+F5. Visual studio 2010 also provides you with three different views for developing web parts. The views are split view, design view and Source view(as we have in designer 2007).The Visual Web part project Item basically loads a User Control as a Web Part.
ASP.Net Web Parts
Where a developer can build up User Interface and logic in a class file. You do not have designer for drag and drop of controls. This web part inherits from standard ASP.Net web part. For Deployment we can again use ctrl+f5 to deploy this web part.