In an article published in the Int. Journal of Production Economics in 1999, authors Kee and Schmidt compare the product mix decision you get from ABC and from Theory of Constraints and find them both lacking. Their conclusion is that ABC gives the best results when overhead and labor costs are completely discretionary whereas Theory of Constraints gives the best results when these expenses are fixed. They go on to suggest an extended model to cover the middle ground.
This is an academic publication, so ease of reading was probably not a goal for the authors. It is long and the models are translated to mathematical representation. Still, it is quite easy to understand.
Since my knowledge of ABC is non existent (the "know I don't know" quadrant of the Johary window Dettmer talks about in the article in my first post), I'll not go into this. The way Theory of Constraints is represented, though, is very troubling in my opinion. It may be that Theory of Constraints has evolved since that time, I'm not blaming the authors but they presented Theory of Constraints as a rigid system that forces labor and overhead costs be fixed. I do not think this is true. Theory of Constraints looks at cost through a different paradigm and so classifies them differently then the traditional cost accounting systems. Since modern day businesses face labor and overhead costs that are fixed and not negligible at all, the basic Theory of Constraints models make these assumptions but if these are actually true variable costs, at least to some extent, a correct Theory of Constraints implementation will have to adapt to that. So I have to conclude the article is based on incorrect assumptions and therefore leads to incorrect conclusions.