The wind farm layout optimization (WFLO) problem is a complex and nonconvex optimization problem. Even though many different heuristic algorithms and mathematical programming methods have been tested and discussed, there is no consensus about which algorithm is the most suitable approach for solving WFLO problems. Every algorithm presents its own advantages and disadvantages in solving different optimization problems; thus, multi-stage approaches may combine the advantages of multiple algorithms and offer superior performance. One multi-stage approach used for solving WFLO problems is to apply an algorithm in the first stage to produce an optimized layout which serves as the initial condition for a second-stage algorithm to perform further refinement. This paper presents a comparison between two types of multi-stage methods: the Heuristic-Gradient-based (H-G) model which consists of a heuristic algorithm in stage 1 and a gradient-based algorithm in stage 2 and the Discrete-Continuous (D-C) model which consists of a heuristic algorithm in the discrete scheme in stage 1 and an algorithm in the continuous scheme in stage 2. Annual energy production (AEP) is used as the objective function while the computational time associated with each approach is documented. Three scenarios are investigated in this paper with different complexity in the wind conditions. It was observed that the D-C models provide the optimal solutions with an average of 0.67% higher AEP and an average of 6.2% lower computational time in comparison with the H-G models. The results from this study provide a basis for selecting a proper optimization algorithm for solving WFLO problems which can lead to a significant increase in the overall annual energy production and a large reduction in computational time.