Ok...this has been done to the death but here goes....
I have used both....and I found both to be useful...but if I had to choose one, I would definitely go with Destroyer. There really is no substitute for Destroyer. What you have to realize, and this is ESPECIALLY true for chem and ochem...is that ~90% of both subjects can be encapsulated with about 150-200 core questions (for DAT purposes). After that point...the nature of questions seems to repeat itself and is merely one variation of another with slight modifications. The destroyer does an excellent job of bringing together core problems that will serve as a foundation. Once all questions have been fully digested...you will be able to easily approach a wide variety of questions.
Another thing that is important is balance...this is where Destroyer comes in. One thing that I noticed from achiever is that the questions in gchem were heavily biased towards the quantitative end. While being able to rapidly solve quantitative problems is important....overall balance with conceptual/descriptive chemistry is important as well. Achiever gchem lacks so many things that are drilled in the Destroyer. Furthermore, with ochem...there is almost nothing dealing with laboratory analysis, and STEREOCHEMISTRY. Having put in a lot of time studying organic chemistry, I can say that Achiever ochem alone is not sufficient for giving you a wide range of core problems.
Bio is probably the exception where you need multiple guides because it is such a broad area. For the record...I found both achiever biology and destroyer biology to be very helpful.
Now...how do you know if you're comfortable applying what you learned in Destroyer? That is where achiever comes in. To decrease test taking anxiety and to alleviate factors that are independent of exam material (jitters, blanking, format, etc). All in all....achiever is worth buying for the PAT alone!!!
Overall...I'd say that Achiever falls short in serving as a guide...but going through it was an excellent experience. Destroyer on the other hand is multi-dimensional and serves as a broad learning tool and guide as well. Hope this helps.