I decided to go for the architecture of Option #2 for Infiniforms, as it provided a great way to separate the UI from the business logic.
An advantage of this is that the API Servers can scale independently of the web servers. If you have multiple clients, then the websites will not need to scale to the same extent as the web servers, as some client swill be phone / tablet or desktop based.
This approach also gives you a good base for opening up your API to your users, especially if you use your own API to provide all of the functionality for your website.