Windows Authentication :As you will be using the login & password used in a domain... If you use windows authentication, your webapp will (generally) have to be deployed in a network server and all your users should (generally) have a login created for them in the domain. Though cross domain operations are possible, primarily you wont be able to use it in non-domain based environment like public websites. It will be tough if you want to include some users who are outside your domain.
Forms Authentication : Here you are deciding to act independently. You will assign each user a separate userId and password and will manage them yourself. The overhead here is you should provide and restrict the ways users are created and removed. Here you are not restricted to any domain. For any user to gain access to your webapp should get registered with your webapp. This is similar to any mail sites you see on internet