Going in length ways with the trench will result in moving and disturbing a lot less dirt, my preference, however some times room is an issue of a property line behind the dam, or geographical limitations, say there is a deep holler or solid woods, you will need a good bit of space to store dirt while you excavate wide and deep enough to get good sealed dirt on bottom and both sides.
doing it sideways results in having to move considerably more dirt as sloping it back far enough to be able to drive a machine into and out of the excavation can be a pretty big hole in a good sized dam.
As far as the existing water in the pond, it may need to be lowered some but a couple buckets of clay inside the end of the cut, temporary dam, will usually hold it back well enough while you work, so that you wont lose all of your fish, if you have any in the pond. Hope that helps. Everybody have a blessed Easter!
