The applicability of two Reduced-Basis techniques to parametric laminar and turbulent incompressible fluid flow problems in nuclear engineering is studied in this work. The Reduced-Basis methods are used to generate Reduced-Order Models (ROMs) that can accelerate multi-query problems often encountered in design optimization and uncertainty quantification. Both approaches are intrusive and utilize Proper Orthogonal Decomposition (POD) for data compression. The accuracy of the two methods for reconstructing the velocity, pressure, and turbulent eddy viscosity fields is assessed. The methods are classified based on how many reduced equations are involved. The first approach, often referred to as POD-FV-ROM, only solves one equation with additional physics-based approximations to relate the reduced pressure, velocity, and eddy viscosity fields. The second approach solves two equations and relies on a supremizer stabilization technique. Both methods are reviewed in the finite volume setting and are tested using transient problems: a backward facing step case with an inlet and outlet and a molten-salt closed-loop case. Extension of the methods to parametric reduced-order problems for uncertainty quantification purposes is presented. Conclusions, summarizing the advantages and disadvantages of these two approaches, and recommendations are provided.