Quickest way to circulate outside air thru house?
Moving air tends to feel cooler than still air. If you can put up with the noise, the box fan trick works quite well.
In my experience, air movement in the home depends on air movement outdoors; if it's a still evening, even with lots of windows open, you won't get much air. On the flip side, even a small breeze can help.
If you have lots of money and live in an amiable climate (cool, dry nights), buying a modern whole-house fan may be a good fit. Modern units suspend the fan itself from the rafters via an insulated duct, and are much quieter than they used to be.
As Jimmy Fix-it commented, the best thing to do is to try both of your methods.