Hi there, just want to confirm that the 2013 battery (7150mAh) does indeed work in any macbook air from 2010 to 2013 inclusive. I have mixed batteries from all the wedge shaped MBAs, and currently have a 7150mAh (2013) installed in a 2010 MBA, and the 6700mAh (2012) installed in another 2010 MBA.
You will get a small increase in battery life, however obviously nowhere near as much as the actual '13 MBA because it's the lower clock Haswell processors that allow this.