One way to clarify your query as to when to choose edge and when to choose edge trigger would be :

Case 1 : Edge Trigger
An emergency condition triggered by a low going pulse event. The pulse could be a short transition from high to low and then back to high.

Case 2 : Level Trigger
A latched Emergency switch signal that goes low and remains low till the user releases it. As long as it is not released, the ISR loop is valid.

I am sure there must be a more academic explanation to your query ;-)

Raghu