If a dam collapses catastrophically, the entire volume of the lake is released in one 'pulse.' This means the downstream area will be subjected not only to a wave of great height but also of great peak power (energy per unit time). That's a BadThing(TM) . You could look up info on what happened eons ago when Ice-Age ice dams gave way in the Northwest United States. Canyons were carved out in hours.
If a spillway gives out, then, depending on just how it fails, there'll be a gradually increasing flow rate as the new escape channel is widened. To a limited extent this means the same total water volume is released, but over a longer time period -- again unless at some point the spillway hillside blows out catastrophically. So the peak wave height and the peak power will be smaller, albeit applied for a longer period of time.
Either way, you will not be happy if you're downstream.