Maggie's first book
There are significant differences of the two methods of Maggie Moore and Dave Mallinson:
(1) Maggie Moore does not give hints about the fingering for the tunes, the learner (even a total newbie) has to invent her/his fingering (strategy).
On the other hand in Dave Mallinson's tutor book very elaborate fingering is presented.
(2) Instead of fingering Maggie Moore gives the button numbers throughout in her books; that is, locating the buttons to press is easy.
Dave Mallinson gives the button numbers only for the first 6 (or so) of tunes; instead, fingering instructions are given for all tunes.
(3) The speed/tempo of the tunes played on the accompanying CDs of the Maggie Moore books is much slower; no need for slow-downer.
(4) The number of tunes in the Maggie Moore book is manageable. It's impossible to learn all the tunes from the Dave mallinson's book: they are enough for years.