It really isn't a match without the vertices matching due to the limitations of precision, but snapping of the vertices that "matter" mixed with visual matching for other vertices or the edge between them might look good. But if your question is how to make two lines actually edge match easily, you can try using the Integrate tool, setting up a topology and validating it, or if there aren't many inserting additional vertices and snapping. In 9x there was a zipper tool. Alternately you could try copying and pasting one line into the target and deleting the old or tracing the other line and if needed manually attributing the line or using spatial adjustment to transfer attributes before deleting the old.
