The discussion between those two similiar technologies are very long, and no one is better than other, only is for two different things.
On the ASP.NET WebForms (classic ASP.NET) you have a lot of controls, an extense collection of controls which you can pick, drag and drop and configure, its really fast but you have a lot of impediments when you want to manage at lower level the html of the page, and the code are very disordered.
On ASP.NET MVC you a lot of control on your html and you can do almost anything, i mean anything with styles and html but mostly you need to do by hand. But one of the great advantages of MVC is de order of the code, you always have ordered solution, projects, and clases, its a really great pattern.
Finally do not care to have different projects with different technologies, its a common case, most than you think, and if you think that MVC is better for the new project go ahead, its a really good choice.
I'll hope this help you. I'm a teacher of web development on the course 10264