It depends a lot on how the classic asp app is structured.
The server tag mixed in with HTML is similar to asp.net mvc but MVC is not as messy (or not supposed to be). You might be able to move the classic asp presentation code to a MVC view easier than to a web form. Also classic asp apps were usually developed with the statelessness of the web in mind. There probably is not anything in your classic asp that matches postabacks or viewstate. Classic ASP also uses normal html elements as opposed to asp.net webform controls. In these respects it matches MVC a lot closer than webforms.
If you do not know asp.net webforms or asp.net mvc I would say MVC is the way to go.
If you know webforms very well and don't know much about MVC I would say webforms is the way to go.
But, if your client for some reason does want a redevelopment of the site I would say go with MVC. It's always nice to have a client pay for part of your experience development as long as you can deliver.
On another note I'm always taken aback when I come across a client who wants me to do work on their classic asp site. In every single case the site is a mess. The worse part is that they are usually filled with huge security holes.
