You trade off damage (Shiv) for attack speed (Runnans). In which, Ashe has one of the highest base attack speed in the game. Base =/= passives from ability passives and leveling.
So you are trading 5% (Runnans) attack speed for 160 damage on five units (Shiv). It also scales with crit damage. (Shiv) Runnan's does nothing for you when split pushing either if you are 1 v 1.
Otherwise you trade 160 damage on five units (Shiv) for 100% (No additional damage), 40% AD, and 40% AD respectively on three units (Runnans). Also, for application of slows.
Summary:
Runnan's is more for team fights to apply slows and speed.
Shiv more for split pushing, 1 v 1, and taking more advantage of her crits.