The issue here is that MC stores playlists based upon a unique ID number that is assigned to each file at import time. These are different on different computers. Of course MC knows the full file path of each file also. But, if your file paths are different on each computer, then a playlist from one computer doesn't make sense on another.
You can export playlists on one computer and then use a text editor to substitute paths. This can help quite a bit with one or two playlists.
If you are going to do a bunch, then you should probably do a full database backup and restore. When you restore the database from one MC installation onto a different computer with a different drive letter, you will have EVERYTHING. All albums, all songs, all playlists, etc. But the file paths will all be wrong. All you have to do is use the Rename Move and Copy files tool (RM&C) to change the file paths and *presto* everything will work on the destination computer with the different drive letter.
I've used this technique many times. I periodically copy my main library from my Mac to my Linux music server on a portable hard drive. I also save a copy of a database backup along with it and do the process I've outlined above. Even though I'm changing drives, paths, and even operating systems, it all works. This is one of the many super powerful features of the MC architecture.
Brian.