The math measures are all based on content standards. The Proficient Math tests are aligned more closely with the Common Core State Standards, while the Basic Math tests align with the standards for the National Council of Teachers of Mathematics. In addition, the Proficient Math tests are a bit more challenging.
The Common Core Standards or ones similar are widely adopted across the United States, and for those states that do not use Common Core, the National Council of Teachers of Mathematics standards are frequently adopted.
Both of these types of math tests are standards-based rather than computational/application based. They were all created to address the content standards as published by these two national bodies.
The CCSS in Mathematics have quite a bit in common with the NCTM Focal Point Standards which pre-date them by a few years.
Another difference between the easyCBM Basic Math and Proficient Math tests are that the Basic Math measures are, by design, written to be more accessible and easier than the Proficient Math measures. Therefore, they are most appropriate for use with students who are really struggling and are performing below their grade level peers in math. The Proficient Math tests may actually be a bit too challenging for students who are performing far below grade level expectations. In these situations, teachers may find it useful to use the Basic Math measures until students make sufficient progress to perform at or above the 40th percentile before switching to the Proficient Math measures for regular progress monitoring.
In terms of the better choice, it depends on what standards they align their curriculum and the skill level of the students being monitored. If they are teaching to the Common Core State Standards, then the Proficient Math tests are more appropriate. However, for students who are really struggling, they may find the Basic Math tests more sensitive to monitoring growth.