Even if you can't cut into the hill sides, a nice concrete emergency spillway can save your butt...
Rainman makes a good point. Even if you end up needing the spillway to run down the back side of the dam because of surrounding hills, a person can always use concrete or rip-rap for the water to run over to prevent erosion.
My old pond has only a spillway ( I may put a pipe in next summer and raise the water level a foot so this may change) and it can have a pretty good flow of water over it during large rain events. Most cattle watering ponds in our area have simple spillways that run out into pasture grass. It is very common to see that over many years a ditch erodes and lowers the pond level. I used rock and shaped the overflow so all the water runs over the rock. So far at least, no erosion. And if there appears that some will start at the margins, I'll add more rock. If I end up putting an overflow pipe in, will rework this area down to clay and cover it up to be part of the dam and a new emergency overflow will be in another area.
Point is, with rock or concrete water can be controlled so it does not erode the dam when leaving the pond. Costs a little more, but if you need it you need it. If your emergency overflow runs out over a fairly flat area not prone to severe erosion, then likely a grassed area would be fine.
Remember, the emergency overflow is only used in the most severe of rain events where the main overflow can not handle it. In my case and our 3 acre pond, we had 12" rain in 48 hours and water came within 1" (witnessed by the debris line) of utilizing the emergency overflow, but best I can tell no water ran over it (I was gone and only seen results later).
