Shoud I upgrade to Safari 6.1?
Upgrading to latest software version is generally a good idea for security and performance reasons.

Specifically Safari 6.1 brings its lot of security fixes: http://support.apple.com/kb/HT6000?viewlocale=en_US&amp;locale=en_US.

In terms of functionalities, Safari 6.1 brings the following:


Shared Links: See links shared by people you follow on Twitter;
New sidebar (Reading List, Bookmarks and Shared Links to the left of the browser; can be hidden);
One-click bookmarking;
(Performance enhancements) Safari Power Saver: Only play content from accepted plug-ins;


See more here: http://www.macrumors.com/2013/10/22/apple-releases-safari-6-1-for-mountain-lion-with-shared-links-new-sidebar-power-saver-and-more/.

Whether you should upgrade to Safari 6.1 is up to you. I recommend you do.