Move by move or Chess explained?
Probably depends on the specific book. One thing that is generally true: the Chess Explained books are older. Also, I think that the move by move opening books are mostly repertoire books, whereas the Chess Explained books try to consider a variety of possibilities for both sides. Here are two reviews for comparison. (This is one case where the Move by Move book is not a repertoire book.)
The English: Move by Move by Steve Giddins (2012)
https://web.archive.org/web/20140627105428/http://www.chesscafe.com/text/hansen161.pdf
https://www.newinchess.com/media/wysiwyg/product_pdf/7129.pdf
Chess Explained: The English Opening by Zenon Franco (2006)
https://web.archive.org/web/20140626234756/http://www.chesscafe.com/text/hansen104.pdf
http://www.gambitbooks.com/pdfs/Chess_Explained_the_English_Opening.pdf
That is just one example. In all cases, I think it is best to try to examine available online resources. In this case, the parallel turned out to be between two books of more or less the same type, but, as I previously noted, there are often important differences in purpose from one book to another on the same opening. The usual Move by Move book is a repertoire book intended to make choices to help the reader play one side of an opening.
The Sicilian Taimanov: Move by Move by John Emms
https://web.archive.org/web/20140626221508/http://www.chesscafe.com/text/hansen162.pdf
https://www.newinchess.com/media/wysiwyg/product_pdf/7070.pdf
is intended to offer suggestions for Black on how to play the Taimanov.
Chess Explained: The Taimanov Sicilian by James Rizzitano
https://web.archive.org/web/20140626170002/http://www.chesscafe.com/text/hansen92.pdf
http://www.gambitbooks.com/pdfs/Chess_Explained_the_Taimanov_Sicilian.pdf
is intended to help both White and Black.