With the new version of SharePoint the guys in Microsoft did a lot of improvements. One of these is the improvements about the database.
The new SharePoint 2013 taking advantage of MS SQL 2012 Server functionality and using shredded storage that reduces the size of content database and optimizes network traffic.
Off course you can use SP 2013 also with a MS SQL 2008 R2 SP1 database.
In Microsoft has remove a lot of redundant and unused table and they has simplify the database schema and optimized data access to improve the database performance. Take a look at the keynote video http://www.youtube.com/watch?v=BLsIjvIyAxo at 1h 21m.
The shredded storage reduce the amount of data that is saved and reduces the amount of network traffic between the SP web servers and the SQL servers.
One of the most painful feature in SP2010 was the versioning feature. In SP2010 the versioning does not worried about the changes between the previous version and what you start to upload. It just get your new one document and put inside the database. So if the old document was 100-KB and the new one is 105-KB you will have 205-KB of documents inside the database.
In SP2013 by the MS-FSSHTTP protocol only the changes made while editing a file are stored in the content database. By the Office Document Cache, that was used in SP2010 too, the system is able to check the difference between your version and the version in the content database and send to you just the difference.