iPad mini retina vs iPad Air performance

So we all know that the iPad mini and Air both have the A7 chip. However, with the iPad Air's larger battery size, the battery life for both devices is supposedly the same.

The only meaningful difference in both devices' hardware is only the screen area and battery capacity, which leads to 2 possiblities:

1. Purely the difference in screen areas makes the battery life of both devices about equal despite the mini's substantially smaller battery.

2. The mini got the underclock and performs slightly slower than the Air, in order to have both devices get about the same battery life.

Personally I'm hoping the answer is 1, because (duh reason) I'm buying a mini. 2 is still a possibility though. Do you all think that the mini has been underclocked? If so, by how much?