Clayton Croy's "A Primer of Biblical Greek" and Machen's "New Testament Greek for Beginners: Second Edition" share enough similarities that I would be very surprised if Croy's book was not based on Machen's first edition. I have worked through 10 units of Croy, and have looked ahead through unit 15 to make these comments, and so my comments correspond roughly to the first half of each book. I have read through Machen's 11th lesson, and have completed all Machen's Greek-English exercises (most w/o writing them out) through unit 9.
Introduction of grammatical subjects is virtually identical.
Croy seems to introduce a little more vocabulary than Croy. In the first 15 units, there are less than 20 words in Machen that are not found in the corresponding unit of Croy. All of these words do occur somewhere in Croy, just not the corresponding chapter.
I would say Croy presents the grammar in a considerably more approachable fashion. Machen is not bad. Both might be considered on the brief side by some students. The online Koine Greek course taught by Professor Laura Gibbs (most course materials online at time of this writing) provides supplementary commentary keyed to sections of Croy's textbook.
I find Croy's invented sentences are much more useful than (most) of Machen's; Croy's sentences are longer and use the grammar presented to a better degree. Machen sentences are often briefer, with less of the more elaborately constructed sentences per chapter. A number of Machen's sentences might better be described as 'drills' (simple constructions to reinforce that chapter's grammar). Croy has no "drills". Croy's use of LXX and NT sentences in every chapter is one of the main reasons I chose his book, and there is nothing like this in Machen.
Almost 50% of Machen's exercises are English-to-Greek. Croy provides only a half dozen English-Greek exercises in each chapter. Anyone who finds English-Greek translations useful in language acquisition will be disappointed with Croy's lack of exercises.
My overall appraisal: I purchased Croy, and would recommend anyone choosing between these two texts do the same. However, if you can get Machen from the library as I did, photocopying the exercises may be useful. Most Machen's exercises are simple enough they can be done on public transit or other places where it may be harder to go through Croy. Machen's Greek-English exercises could serve as a "preliminary" set of exercises, leading up to the sentences in Croy. Anyone that likes practicing with English to Greek must supplement Croy, and due to the very similar vocabularies, Machen would be ideal.
Hope these comments may be of assistance to folks looking for, or teaching from, introductory Koine textbooks.