Integrating web applications

What you guys think the best approach to integrate web applications?

Lets assume we want to build a ecommerce, so we need something to
generate the pages and a billing system, so we could use radiant and
spree, i know that spree can generate the pages, but lets assume that
radiant would be better, more flexible, powerful and so…

With Rails 3 we can mount applications or we can create the systems
exposing all the functionalities as a API.

With frameworks, you have more flexibility because you have the code, so
you can do whenever you want, but this cost you time, complexity and
issues related to update to new versions of the framework.

With API, you dont have flexibility, what you see is what you get, the
API is predefined, but integrating with others systems is just a matter
of calling a webservice, multiplataform, multilanguage and dont need
worry about updating verions and so.

I have this dilema, so what you guys think about this, API or Framework
or depends?