Gen Choi's single book on TKD

I know that the single edition of Choi's TKD is not a condensed encyclopedia prior to the 15 edition of the encyclopedia and a condensed version afterward. I have a copy of the 1968 version and of the last condensed version. The question that I have is what are the differences in the different versions (in brief)? What versions do you prefer? Are some version more conductive to a pre-sinewave understanding? and a post sinewave understanding?

I am not sure of your question.
Gen Choi wrote a book on TKD, the 1st ever for that matter. It was dated 1959. Then in 1965 he made the 1st English book ever on TKD. This one contained only 20 patterns & still had a lot of karate influence in it as well. There is no 1968 book. You probably mean the 1965 book, reprinted in 1968 or dated that way for some similiar reason.
Next came the 1972 book, which we called back then the "bible of TKD" as it was unlike any MA book ever produced up to that point in history. Everytime I posted that, no one ever corrected me, so I guess that claim still stands. What makes the 1972 book, which had 6 editions & a reprint or 2, till 1986, was that it contained all 24 patterns & most of the ITF TKD terminology that we do today. It also contains most of the techniques we do today.
The 15 volume Encyclopedia that he wrote in 1983, 1st edition dated 83, but came out around 1985, is unlike any written work ever on any MA, as far as I know. Please correct me if I am wrong. This work has a single book on 3 patterns each or the 24, proving such detail that they make an invaluable teaching, training, education & reference tool for any serious Chang Hon student or instructor (I know all instructors are still students LOL). Even if one is not a Chang Hon student, the other 7 volumes also make this a must have for serious students of any TKD, imo.
From there a condensed version was produced that allowed students to carry a single volume. It lacks the very detailed step by step beakdown of the patterns as the main difference.
The big differences imho is the movement away from karate that is shown throughout this series of excellent, all of which are both 1 of a kind AND the 1st of their kind! In addition, the scientific basis he tries to lay for his KMA expands as well. For instance, the theory of power in the 65 book contains just 4 elements. In the 1972 book, it expands to 5, with a subsequent edition of that book adding the 6th & final aspect or element. Of course the 15 volumes adds SW & Juche Tul. With later editions adding his final techniques he created or he had added to his KMA.

Well, I have to say neither single volume is preferred. Only the 15 volume set contains the details vis a vis pattern move application examples, foot diagrams, and photos from numerous angles. Since I have the 15 volume set I have no idea what the condensed text shows vis a vis sine wave. However, flexing the knees has been a staple for some time. Post 1983 texts used the metaphor sine wave to describe the up / down (down / up / down motion) and had more illustrations to show what was intended.