What are the pros and cons of Double Butted vs Straight Spokes when building a wheel?
In his book 'The bicycle wheel' Jobst Brandt, says that double butted spokes will be more resistant to fatigue failure when built into a wheel. 

This is because spokes break because of the cyclic stress they suffer as the wheel rotates. 

As the spoke rotates thru the bottom of the wheel it experiences a reduction in tension. 

Butted spokes are more elastic so this reduction in tension is spread over more spokes, each experiencing a smaller reduction in tension.

Wheels are an order of magnitude stiffer than the tyres they roll on, so any stiffness differences will not be noticeable. A wheel built with butted spokes will be able to carry a heavier load before any of the spokes become slack. At this point the rim is no longer restrained and the wheel will be more likely to collapse.