This quick comparison sheet gives you all the info to decide whether to use Cocos2D 1.x or Cocos2D 2.x. Contrary to most programs, a higher version number doesn’t infer “better” or “more”. There are pros and cons for both versions.
At the time of this writing the decision really only boils down to whether you want to use shaders and whether you must be able to deploy your app to 1st & 2nd generation devices. See for yourself, it’s that simple:
(+) compatible with all iOS devices
All other differences to this day are minor, and most new features and bugfixes have been migrated back and forth between versions. For beginners I strongly recommend using v1.x as there’s a lot more documentation available for this version. Those who have no interest in writing shader programs can also safely use the v1.x branch without missing out.