No Discernible Effects
Only one of the seven studies met the WWC's criteria with reservations.
Resendez & Manley (2005) reported no significant effects of the Saxon Elementary School Math program on overall mathematics achievement at grades 1–5. Using school-level data provided by the authors, the WWC confirmed that Saxon Elementary School Math did not have a statistically significant or substantively important effect on math achievement at each grade level from first to fifth grade. Based on this study finding, the WWC categorized Saxon Elementary School Math as having no discernible effects on overall math achievement.
The average performance gain was +7 percentile points which is not educationally significant. Compare this to the average gain of +12 percentile points for Everyday Math.
For both math programs, most of the results were not statistically significant.
I'd say that a school district has little basis to switch from whatever it is they are currently using to either of these math programs based on the research reviewed by the WWC.