I think I have a quicker way of aligning dublicate UVs on top of each other using vertex snapping (crtl + shift + tab):
1) select one island (L) and snap (shift + tab) one matching vertex pair together ; orientation doesn't matter in this step !
2) select the matched vertex Crtl + S cursor to selected
3) choose 2D Cursor as pivot point for rotation and rotate (R) to match a second pair of verts by snapping them onto each other.
This lines up both objects perfectly. Any missmatch between other verts is due to numerical errors using "unwrap" (i.e. the shapes were not perfectly identical)
