In this study, we present and discuss several original sets of jump interface conditions for the coupling of multi-dimensional models in fluid-porous systems with arbitrary flow directions. There are issued from the theoretical derivation carried out in Angot et al. (2017) using the generalized Darcy-Brinkman equation in the free flow/porous medium inter-region Ω_fp and a suitable asymptotic analysis for the dimensional reduction to a dividing surface Σ between the free-fluid Ω_f and porous Ω_p regions. The macroscale models can be either the Stokes/Darcy or Stokes/Darcy--Brinkman coupled problems in the fluid-porous systems, so covering the whole range of porosity 0 < φ_p < 1 of the permeable medium. All sets of boundary conditions include jumps of tangential velocity vector and/or stress vector either at the top surface Σ_t or at the bottom surface Σ_b of a transition layer Ω_fp. Besides, in all the latter jump conditions, the inherent tensorial form of the stress jump condition ensures to handle flows over anisotropic porous media. In the present study, all these interface conditions are validated and calibrated against three benchmark problems including pressure- driven or shear-driven flows. The reference solution is obtained by the numerical solution of the single-domain continuum model computed by a second-order finite volume method. This allows us to calibrate the slip velocity α_Σ and stress jump friction β_Σ coefficients that must be non negative to ensure the mechanical energy dissipation. Then, it is proposed for both the Stokes/Darcy--Brinkman and Stokes/Darcy coupled problems, an optimally accurate stress jump interface condition associated to the velocity continuity on a suitable dividing surface Σ = Σ_b, that minimizes the loss of flow rate. The comparative performance results clearly indicate that the latter interface condition on Σ_b tremendously outperforms all the others. Moreover, all the related coupled problems are shown to be globally dissipative over the full range of porosity which ensures their mathematical (at least formally) and physical stability.