In the discussion of Planck and Mach, it should be considered that Mach was an empiricist, who had partly auto-didactically trained himself before his formal education and furthermore trained in a handicraft as a woodworker, while Planck was of a theoretical bend, declining for himself the 'need' to do empirical research. This seems important as Mach brings the experience of trial and error, tinkering or 'bricolage' to his theoretical and metaphysical views of (the development of) science.
Planck disagrees with his interpretation of Mach's historio-critical view of science at the beginning of his (Planck's) "Survey of Physics" because Mach tries to build his concepts of (physical) science on the notion of fluidity of human knowledge and the limits of models made up by (wo)man, which Mach sees as a currently 'valid' thought economic conceptualization of the known facts (and supporting assumptions resp. theories). Planck understands these as 'more or less arbitrary' constructions (which, I think, they are not as they are historically developed and take account of the currently known facts 'arranged' under the needs of specific world-views of scientists).
Furthermore, Planck disagrees with Mach's basing science in sense-perceptions (which are nevertheless deemed a useful starting point and correction to former exaggerations based on physical research results), but favors a view based on the 'constancy' of the properties of reality, a constancy which persists through all individual and historical interpretative variation. If I am not mistaken (pls. correct if I am wrong) Planck favors a statistical approach to (re-)searching these constant properties of reality, e.g. endorsing Boltzmann's thermodynamics in this context.
(N.B.: To me it seems Planck reduces the notion of Mach's perception complexes, which link properties of reality and their representation in the mind through mutually dependent functional complexes. Even if we use 'modern', extended sense-organs such as microscopes and Large Hadron Colliders, these measurement instruments can, just like our senses, only react to and register what they are 'designed' and constrained to capture - which leads us to issues with particle-wave dualistic appearances of entities.)
In contrast, Mach uses the 'historic-critical method' developed by religious scholars at the University of Tübingen, who put statements from the bible in their historical context, see e.g. his "Science of Mechanics. A Critical and Historical Account of its Development." As indicated above, Planck sees the world differently, where the standard of scientific research should be to strive for 'a fixed world-picture independent of the variation of time and people'. He argues that (physical) theory can be built on more 'fundamental' and unchanging concepts such as his Planck constant. Science should (can?) derive fundamental, stable statements or truths in his view.
I do see how Planck's approach works for abstract constructs as theoretical *pictures of the world* - one can build axiomatic, theoretical systems that capture (or seem to coincide with in a more critical reading) observed facts. However, I do not see how this works on a larger scale of several generations of practical researchers and theorists building their theoretical systems based on what they deem fundamental facts - which usually tended to change over the human history of science (which leaves us with the question: are Planck's constants and constancies subject to change?).