I have been using Comodo Dragon browser for the last two years, no problems at all.

Comodo Dragon is based in Chrome but with added privacy, they strip part of the data being sent to Google. There is another version called Comodo Ice Dragon based in Firefox with added privacy that I have never used.

Having said that, if you are concerned about privacy is much more important to hide your computer IP with Tor or a VPN than it is using a better browser.

http://browser.comodo.com/