In the present work, different computational implementations of Phase-Field Fracture implemented in a FFT-based environment are compared. Firstly the problem is solved with an implicit staggered method, which independently solves the equilibrium and Hemholtz type damage equations, obtaining the strain and damage fields by means of an hybrid iterative procedure. Then, a Newthon-Rhapson method is used for solving the problem in a monolithic way. A path-controlled scheme is also combined with the Newthon-Rhapson method and compared with the above methods to determine the existence of effects such as snap-back [2] that the others methods can't determine due to being implemented with strain-control. As case studies, the results of brittle fracture in 2D and 3D pre-cracked domains are presented, comparing the resulting force-displacement curves of each method and comparing the number of iterations performed, simulation time and discretization size to determine the effectiveness of each method.