Question: Yes, I am aware one is a framework and the other a CMS.

However, I am a one man team that develops projects/websites for myself and I have a limited amount of time to get these projects off the ground, so speed is crucial.

Basically I am looking for the easiest and fastest method for creating web apps without being limited on features.

Would it be best/fastest to learn Codeigniter or to build off of Wordpress and develop my own themes/plugins? Possibly another option that would be more viable?

I deal a lot with video/photo media and high traffic websites.

Thanks!

Answer: 
If what you develop is web applications, especially for high-traffic sites, then why not to also consider Doctrine? It is a really good framework for developing webapps. Regarding WordPress - if what you need is mostly webapps with extensive user interaction and complex data structures - WP can't handle that efficiently due to lack of ORM and MVC pattern support (there are a couple of workarounds, but anyway). 

And if you're open to learn new languages - also consider learning RubyOnRails and Django - both are awesome platforms, documented well and having awesome communities.
I agree with tpae. Definitely WP is not meant to be used for web apps. So forget about it.

CI is great, easy to learn, and in combo with [Backbone.js](http://documentcloud.github.com/backbone/) and Phil's [REST\_Controller](http://philsturgeon.co.uk/blog/2011/03/video-set-up-a-rest-api-with-codeigniter) it's a beauty to work with :) You'll be building highly responsive web apps in no time (this sounds like a commercial :D )