I'm about 2 months into a 3 month project which takes the second approach you've outlined here. We use a RESTful API server side with backbone.js on the front. Handlebars.js manages the templates and jQuery handles the AJAX and DOM manipulation. For older browsers and search spiders we've fallen back onto server side rendering, but we're using the same HTML templates as the Handlebars frontend using Mozilla Rhino.
We chose this approach for many different reasons but are very aware it's a little risky given it hasn't been proven on a wide scale yet. All te same, everything's going pretty smoothly so far.
So far we've just been working with one API, but in the next phase of the project we'll be working with a second API. The first is for large amounts of data, and the second acts more like a CMS via an API.
Having these two pieces of the project act completely independent of each other was a key consideration in selecting this infrastructure. If you're looking for an architecture to mashup different independent resources without any dependencies then this is approach is worth a look.
I'm afraid I'm not a Ruby guy so I can't comment on the other approaches. Sometimes it's okay to take a risk. Other times it's better to play it safe. You'll k ow yourself depending on the type of project.
Best of luck with your choice here. Keen to see what others share as well.
