Which engineering branch and its subject content match more with the metallurgy and materials science?

The first thing to realize is that material science is a broad term that encompasses metallurgy and materials engineering.

Materials science, in other words, is the study of materials in all disciplines, including physics, chemistry, and biology. Metals and alloys, as well as their uses in diverse sectors, are the subject of metallurgy.

Engineering, particularly metallurgical and materials engineering, is concerned with the design and manufacture of materials for sectors such as aeronautics, space, and automobiles.

So choose materials engineering or metallurgical engineering if you’re interested in materials science applications in engineering.