Luce: I can’t make any recommendations as yet. Chances are I’ll switch between the two anyway. Meanwhile, Amadeus has made some very perceptive comments. 
Amadeus (vocative?): It took me some time, too, to discover the existence of the chapter-by-chapter wordlist, but now it’s bookmarked for easy access. As you point out, the authors succeed in keeping the reading material uncluttered by other matter, which is a big plus! Athénâze is weak in this respect, though the Italian make-over is more elegant. (As for the Italian text, I treat it as a secondary language course, totally separate from the Greek…).
Yes, there are ‘un-deduceable words’. But once you’ve looked up ‘lightning’ and ‘thunder’ (and are beginning to understand the joke), you immediately encounter ‘lightning BLÉPO’ and ‘thunder AKOÚO’. Aren’t BLÉPO and AKOÚO deducible? I can only say that I found myself instinctively interpreting lots of words (not all of them!) in that first text - which served to enhance my confidence and my enjoyment.
I think Peckett & Munday aimed at keeping ‘ancient’ (1960s) schoolboys amused. (Incidentally, aren’t Monty Python just a bunch of overgrown schoolboys?) Athénâze aims at a somewhat maturer audience and thus chooses a hard-working, ruggedly independent farmer as its hero. However, there are excellent supplementary ‘Athénâze’ materials on the Web that offer lighter relief – involving Socrátes, his much-maligned wife Xanthíppe, Alcibiádes and Alcibiádes’s dog. Choose the Reading Exercises from this menu:
http://web.uvic.ca/hrd/greek/
Mustn’t forget this excellent Thrasymachus site either: http://www.vroma.org/~abarker/thrascontents.html
By the way, Peckett & Munday also wrote two funny Latin books in the same vein (‘Principia’ and ‘Pseudolus Noster’). Here too, the text is kept in a separate section, and there’s a strong oral emphasis. Small informal line-drawings are inserted to satisfy Amadeus, and there is a short section called ‘Carmina Latina’ (some poems by Catullus) where all the notes are in Latin, à la Örberg, [“favent tibi? significat “amant te.?].
Back to Greek. As a beginner, I find myself also learning a lot about Greek from the introductory hints given by those ancient 19th-century textbook authors. For example, check out the first 12 Introductory Remarks here: http://books.google.com/books?id=WqsBAAAAYAAJ&dq=Colson+%2B+Greek
You might need a proxy to read or download.
Cheers,
Int