Depends on what you need. I replaced my 2011 MBA with a 2013 11" i7/8gb/512gb MBA and am very happy. USB3, 8gb and 512gb are all new features that weren't available in 2011. I see noticeable improvements in latency using Logic Pro and rendering in Final Cut Pro.
But when I had them side by side while setting up, I was surprised how little difference there was in "ordinary" tasks (iTunes, Safari, MS Office, even Photoshop). So unless you are using pro applications (or maybe games?... I don't do those), you may not notice much of a performance increase. I never noticed much of a problem with 4gb on my 2011 machine, and I hadn't filled my 256gb SSD however it's nice to have 8gb/512gb now. If you want either of these, then it makes sense.
I don't know about the battery. I was able to get through a 12 hour day with my 2011 machine using common sense power management. And I was getting 4 or 5 hours even with the screen on full and a movie playing. How much does a battery replacement cost?
