AoPS is a challenging honors level class which stresses the importance of problem solving as a part of the learning process. Students are presented with challenging problems and then work to apply the knowledge they have from past situations to find new and better solutions. Students discuss and solve problems in class, and homework generally consists of similar, but more challenging problems that stretch their thinking and creativity in problem solving. This is a good option for students who find math easy and tend to get bored with a traditional program.
Dolciani-based math provides instruction through examples, opportunity for practice in a group, and then 20-30 practice problems completed using DeltaMath. The class provides many example problems and students are asked to work on similar problems in the homework, using repetition to master the concepts and skills. This class is a good fit for students who need more practice and repetition with concepts.
Both will provide an excellent education and either program will prepare students well for future math classes.