- You host the server
- You pay for your server and have to keep the web server (Wordpress.org itself is free to use though)
- You get your own domain name
- You get more flexibility, range, and options (plug-ins, themes, and code)
- You can add in ads and make money from it
- Recommended by a majority of websites over Wordpress.com
Wordpress.com
- Wordpress hosts the server
- Cheaper/free
- Domain name includes Wordpress.com
- Can't have custom themes
- Hosting service ranges from $36-$5000 a month
- Automatically backs your website up for you
- There is ads on your page, but you don't get money from it
- You can't see any statistics of your page
- They have the power to delete at any time if they think it goes against their policy
Conclusion: Most websites prefer Wordpress.org because it's gives you more free range to do whatever you want, and in the end it's probably cheaper then Wordpress.com, you just need to keep up the site yourself.
Sources: themes.com, wpbeginner.com