Is logic board from Macbook Air 11" A1465 2015 compatible with Macbook Air 11" A1465 2014? I am thinking about buying this logic board and putting into into my Early 2014 11" Macbook Air, which has much lower specs.

Will it work?
For these models the answer seems to be yes. 
According to an iFixit thread you can even exchange it with the 2013 model.

In general though, you have to be careful since Apple tends to make minor changes, making the models incompatible. 
For example: They changed the battery connector in the iPhone 6s from its predecessor, the battery itself was basically the same.