***Note this post applies to Power BI for Office 365 (deprecated as of 12/31/2015). Though some concepts remain the same or similar, all details are not necessarily applicable to the new Power BI V2 service.***
There's several important differences between a site set up in Power BI for Office 365 (SharePoint Online) vs. a Power Pivot Gallery in SharePoint on-premises. One key difference I want to focus on now is how you can organize the Power BI site.
With your Power BI site, you can set up various document libraries within the site and they will all show up on the Power BI app page (i.e., the "app" view in the browser rather than the regular doc library view - see this if you don't know what I mean by that statement). Different document libraries can be used to organize content based on subject area, functional area, or whatever makes sense. The document libraries can also have separate permissions (which might allow you to set security at the document library level which is far less tedious than managing it at the individual file level). When it comes to content arrangement & permissions, the same planning you would have put into structuring SharePoint document libraries still applies. Here's an example of how a Power BI site looks with various document libraries within the same site:
With a Power Pivot Gallery in SharePoint (on-premises), it's associated to one single document library. So, the ability for the Power BI site to display content across various document libraries in the site opens up lots of possibilities.
You can also create subsites if that would be helpful from an organizational or permissions perspective. Individual subsites do get their own unique Power BI app page, but they share the same Power BI Admin Center.
One last thought for you - notice in the screen shot above how there is a document library for "FAQ and Help." It's got a > symbol at the beginning of the name to ensure it's sorted at the top. Something like this is a great way to deliver documentation to your users. (Hint, hint.)