I'm not working in material sciences but as a (particle) physicist I came into touch with solid physicists a lot. To elaborate: In particle physics, one of the main components is usually the scintillator crystal which is a very high advanced material. The material for it for an upcoming particle accelerator was entirely researched by our neighbour working group, means, the theoretical department was involved as well as the according experimental department. I know that the latter consists of roughly 2/3 physicists and 1/2 material scientists. The theoretical department is mainly composed of physicists with a few mathematicians alongside. However, in addition that a new chair of the theoretical department is only involved in finding new materials for the circuits resp. processors for supercomputers and from my impression, according to the welcome lecture, this topic is far away from "material science/chemistry". It is very, very mathematical.
Despite from that, I know some physicists who are working for Infineon who specialized in solid / semiconductor physics. On the other hand, the girlfriend of my colleague owns an engineering degree in micro mechanis and worked for Infineon ~since the beginning of her study but they didn't tookkeep her over afterwards, though she did her bachelor and master thesis there in addition to further researches along her study. They clearly prefer physicists on an official level.
Official, because, as she obviously really wants to stay in this field (and there are no similar companies where she is living), she got her steps into the company again via an engineer personnel service provider (and Infineon is now paying much more for her work as when they would have given her a regular contract in the beginning..).
What I want to add here: It depends on what you want to do on a daily basis, respectively, which tools and in which worlds do you think. I know mathematicians working in optic fields, physicists working as AI engineers, my girlfriend is a biologist and is working as a quality manager and software tester for electromechanical devices for the chemical industry. My boss is a mathematician and supervises a lot of engineers together with a few scientists. To conclude: From my feeling, you should choose material science while, from my pov, a combination of a bachelor in physics and a master in material science/engineering would be the best fit.