Which edge is better for choosing a trigger?
Generally trigger on sharper edges when possible.  That will result in less time uncertainty and therefore jitter.  It also minimizes the time the digital input is held in the in-between region.  Some digital inputs don't react well to being held there.  They can oscillate and/or draw higher current.

When you have unavoidably slow edges, you need to use a Schmitt trigger input.  Those have hysteresis built in, and are specifically designed to tolerate being held at in-between levels indefinitely.