What is the differences in CRM Application Architecture from CRM Online to CRM On-Premises?

Sticking with development, on premise allows for custom developed plug-ins. Online allows for this as well, but with limitations. Plug-ins are sandboxed with limited permissions and can only make requests to same CRM tenant or to external web services. Here again, this really comes down to how much customization you intend or foresee happening via plug-ins.
For all you SQL gurus out there, online does not allow direct access to SQL data; while on premise does. This will limit your development of custom reports to the use of FetchXML for online, while you can use either FetchXML or direct SQL access for on premise. This could be somewhat of an issue, if you have a development staff versed in SQL, there will be a slight learning process for switching over to FetchXML.
CRM Online only offers Claims-Based Authentication and Security where CRM On-Premises offers either Claims-Based Authentication or ADFS.
CRM On-Premises allows unlimited workflows and entities, where Online has a limit of 200 workflows and 300 entities.