Which one is better – wordpress.com or org?

It depends on what you want for your website.  Free and simple or fabulous and advanced?
 
www.WordPress.com 
Pros:

Free
No technical knowledge required
Takes care of spam for you
Takes care of SEO* for you

Cons:

Limited theme designs
Limited widget features
Bad for SEO (WordPress takes the credit instead of you)

 www.WordPress.org
Pros:

Install a fabulous theme

Unlimited widget feature plugins

Lots more control

You take credit for SEO

Cons:

More expensive [...]

Q. How do I install a fabulous theme design on my WordPress blog?

This is one of the most frequent questions I get these days.
Sounds like a simple question, but it can get really confusing and complicated.  If you’re willing to fork in some money and time, you should be able to do it in no time.
But first, you have to decide what type of blog you are looking for.  [...]