Other than the fact that ASP.NET MVC Web Application has more clarity in its implementation of the MVC pattern and that it strictly follows the MVC pattern,
It takes a bit more experience, discipline and work to design an ASP.NET MVP Web Application so that your application supports test automation. When you can slap an advanced GridView onto a page along with a SqlDataSource and bind it directly to a stored procedure you throw your test automation out the window.
A lot of MVP applications are written using 3rd party toolkits that encapsulate a lot of the codebehind logic. That tends to muck up your clean separation of responsibilities in a MVP design.
On the plus side I can write an ASP.NET Web Application with a rich UI using a 3rd party toolkit in a 10th of the time I can with MVC in it's current state. For a simple admin tool that's exactly what I would do today. For a large scale n-tier application I would lean towards MVC.
This recent question may address your concerns: How does the MVC pattern differ, if at all, from the DAL / BLL design pattern?