"My client asked me to come up with a presentation of whether to use to Sharepoint or Wiki or both and how. Our team is an international team with members in New York, Singapore and London. Currently we have a wiki and Sharepoint set up but there is no clear guide/structure of how or when to use each."
This describes how databases, SharePoint, and Wikis should operate. Real life varies. Always remember that we're building processes, not temples.
A database stores structured data. The structure is typically designed and owned by an individual. Politically, it's a dictatorship. Line-of-business applications which gather and distribute raw data are typically associated with databases.
SharePoint provides webs to store lists and documents. Think of this as loosely-structured data. SharePoint lets you control this data with versioning, backup and recovery, workflow, security, policies and auditing. The structure might be seeded by an individual, but ownership is distributed. SharePoint should be designed to unfold according to to will of the distributed owners. Politically, SharePoint provides representative leadership like a parliamentary system though the leaders are typically appointed rather than elected. SharePoint is used by "information workers" to create, manage, and publish information typically stored in lists and documents. SharePoint is used as an interface to databases. SharePoint is a social tool used to recognize and reinforce relationships among people. Through either SharePoint's business intelligence capabilities or its integration with Reporting Services, SharePoint can report on data from structured and loosely structured data stores. SharePoint can index and provide search for structures, loosely structured, and unstructured data stores.
A wiki provides webs to store text with embedded references to media. This is unstructured data. Wiki content can be seeded with the intention to unfold acording to some master design, but politically, it's anarchy. A wiki allow control through versioning and moderation. A wiki is well-suited for collaborative documentation.