WordPress is a blogging platform and SharePoint has a blogging template site. Both offer out-of-the-box capabilities to setup a blog without any programming knowledge but differ significantly in the underlying technology and process.
WordPress Advantages
Developed for blogging specifically and it’s the most widely used platform in use for that purpose. It has thousands of plugins and themes available in it’s marketplace. The plugins are used to extend its core blogging function and the themes provide a wide variety of user interfaces and experiences. It’s open sourced and can downloaded and hosted or you can go to wordpress.com and pay a small monthly subscription.
WordPress Disadvantages
The large number of plugins can also be a problem for a few of reasons. First, wordpress is plagued by malware and virus problems introduced by the plugins. Second, a plugin can break other plugins or the core functionality. Lastly, wordpress starts to break down when it’s used to build larger and more complex types of websites.
SharePoint Advantages
If SharePoint is already installed all you need to do is create a new blog site using the blog template. Since it’s part of SharePoint, all of the enterprise features of the platform are available to the blog, such as search, security, term store, etc.
SharePoint Disadvantages
If you’re only looking to host a blog, the entire SharePoint platform has to be installed which would make it very expensive. There aren’t many third party products to enhance the core functionality.
Technology
WordPress is built with php and mysql whereas SharePoint is a .Net product so enhancements can be built with VB.Net, C# as well as SharePoint JSOM