Magnetic materials in general, such as hard-magnetic neodymium-iron-boron (NdFeB) or soft-magnetic nickel-iron (NiFe), play a crucial role in driving power conversion devices as wind turbines, sensors, and electric motors, cf. [1]. Owing to their relevance for addressing technological and societal challenges, in particular the reduction of CO2 emissions, these materials are being studied intensively. Current research targets improved performance, reduced dependence on critical raw materials, and a lower energy demand during manufacturing and processing. Numerical simulations, and in particular the finite element method (FEM), offer additional insights into the materials mechanisms itself to accelerate the development of these materials. Hence, reliable and robust simulation tools are in demand. Such reliable simulations of magnetic materials require some special care, in particular regarding the discretization of the magnetic field H. In this contribution, two different formulations based on a magnetic scalar potential and a magnetic vector, i.e., the magnetic Gauss law and Ampère's law, are considered to represent the magnetic field. To ensure the uniqueness of the magnetic vector potential, the Coulomb gauge condition is imposed, cf. [2]. This work demonstrates the workability of both formulations, applied to a FEM based micromagnetic framework, in terms of suitable numerical examples and highlights the individual advantages. [1] O. Gutfleisch, M.A. Willard, E. Brück, C.H. Chen, S.G. Sankar and J. Ping Liu. Magnetic Materials and Devices for the 21st Century: Stronger, Lighter, and More Energy Efficient. Advanced Materials, 23: 821–842, 2011. [2] E. Creusé, P. Dular and S. Nicaise. About the gauge conditions arising in Finite Element magnetostatic problems. Computers and Mathematics with Applications, 77: 1563–1582, 2019.