Approach shoes vs. mountaineering boots for alpine rock

Obviously this depends on the terrain, but if you're not expecting any snow, what do you wear on your feet for alpine moderates? Lightweight mountaineering boots will be stiffer and better for edging but approach shoes are lighter but maybe less support, and better for smearing. Depending on the route, you'd probably bring along some more technical shoes, if there's harder pitches. So in general, what do you bring along? Or when would you bring one over the other?

Approach shoes, unless there is very steep snow climbing or Alpine ice. 

For easy alpine rock if the approach is dry, or at least 80% dry and the snow is hard and you re not knee deep in it, I will always take approach shoes, just for comfort sake