We opted for #2 when building gaug.es. I worked on the API (ruby, sinatra, etc.) and my business partner, Steve Smith, worked on the front-end (javascript client).
Pros:
Move quickly in parallel. If I worked ahead of Steve, I could keep creating APIs for new features. If he worked ahead of me, he could fake out the API very easily and build the UI.
API for free. Having open access to the data in your app is quickly becoming a standard feature. If you start with an API from the ground up, you get this for free.
Clean separation. It is better to think of your app as an API with clients. Sure, the first and most important client may be a web one, but it sets you up for easily creating other clients (iPhone, Android).
Cons:
- Backwards Compatibility. This is more related to an API than your direct question, but once your API is out there, you can't just break it or you break all your clients two. This doesn't mean you have to move slower, but it does mean you have to often make two things work at once. Adding on to the API or new fields is fine, but changing/removing shouldn't be done without versioning.
I can't think of anymore cons right now.
Conclusion: API + JS client is the way to go if you plan on releasing an API.
P.S. I would also recommend fully documenting your API before releasing it. The process of documenting Gaug.es API really helped us imp
http://get.gaug.es/documentation/api/
