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I want to add another reason for NOT using a FEN approach to indicate
movement.  Besides making it difficult to check legality of a move, of the
play area is HUGE, then doing a FEN data transfer ends up wasting a lot of
bandwidth to transfer.  Big difference between C4FB:J15FB#M8CV:D120HL##
and do a board for a multi-dimensional space (like that entry indicated
two pieces moving in a 3 dimensional space).  If you were to do a FEN for
that, it would be FAR larger.  Only place where I can see a FEN approach
taking up less space is with a small board with a small number of pieces. 
I would say you use a FEN approach for sending a saved game state, and also
a case of a small board with only a few pieces on it.

By the way, in the tradition of what I see FEN does, you could have a V-FEN format, and then something like what I have discussed with moves, to be bundled together as a stream of data that could be sent from system to another.

I was also wondering how a FEN position would be able to be sent over a web browser, since a / is used to indicate a directory or a file in a directory.