At its core, SharePoint Server (std/ent) is built on top of SharePoint Foundation. The core system is the same and then Server adds in additional templates, features, and services. At its core, SharePoint (Foundation, Server Standard, Server Enterprise) can support saving documents securely in a site. Users with permission to the site and documents can view, add, edit, or delete documents based on the permissions granted to them by a site administrator.
I would say that both Foundation and Server Standard can be a good solution.
From my perspective, Foundation provides a good "workgroup" level solution. By workgroup I mean a small collection of people like a department or project team; 2-25 people. It is pretty effective at that level, but it does not have the more robust features needed to weave a cohesive solution for larger, more complex scenarios which is where Server Standard can come in.
Server Standard offers quite a few Enterprise Content Management (ECM) features that be used to promote very large sites and sets of documents. Here are some examples:
- Content Organizer: Can route documents between libraries or sites based on rules and metadata.
- Document ID Service: Provides a unique ID for that document even as it moves between libraries perhaps based on retention rules or having been moved by a workflow.
- Content Query Web Part: Can be used to find related content based on metadata.
- Content Type Hub (Publish/Subscribe): Provides the ability to publish content types across site collections.
In either case, the system should be designed with the number of items expected in mind. SharePoint can scale to many millions of items and hundreds of thousands of users.