Firstly both are free however there is a distinct difference between the two.
If you are using WordPress.com then they own your website as it is stored on their servers, and you only have front end access to it. You are limited to off the self template themes which they are and they have limited functionality.
In comparison WordPress.org still have the same system however they are entirely customisable in terms of design, build and functionality. You can tailor it to exactly what you want versus a stock standard template that is limited.
While neither is bad having a WordPRess.org site allows for the site to be found in search results and tailored to your business needs.