More gradual.
Further studies on the turbidites have suggested it is more small singular events, such as La Palma. I'd have to do some digging on the latest research from Hawai'i.
On the other, more catastrophist, hand. Simple collapse of a continental shelf might make quite a wave. There is evidence of this happening at the end of the last ice age as Doggerland (Brittan, Ireland, etc.) were being inundated by sea level rise.