Most frameworks are specifically designed to easily handle a large range of applications, while WordPress is quite limited when it comes to using its API to create applications like the one you mentioned. If you want to compare WordPress as a PHP framework with existing popular frameworks, think of it as one of the worst options.
It’s not that you can’t implement certain functionality in WordPress, it’s just that you will do it by writing more and less maintanable code than in Yii, Cakephp, codeigniter etc.
My suggestion is to use whatever you feel more comfortable with. If you’re willing to spend time learning to work with Codeigniter, go with Codeigniter, but if don’t have that time you should probably stick to WordPress.