A key question is whether you are finished drawing one end and just need symmetry at the other end, or if you intend to continue editing the first end and expect the other end to mirror it.
For the former, you can simply select the relevant Edges and Faces at the first end, move a copy to the other end, flip it, and drop it in place. Often you will need to clean up a stray Edge or two or repair a Face if you do it that way, but it is fast and easy.
For the latter, though, you need to do something like Dave describes because you need both ends to be instances of the same ComponentDefinition, just flipped. But you will have to explode the board and the ends and then recreate the board as a single component when you are done else you will get the kinds of cut list issues he describes.
Steve