Particle sedimentation under a turbulent flow is a fundamental problem that has numerous applications in natural and industrial processes. In particular, the motion of anisotropic particles yields complex dynamics whose features are not completely understood in the presence of inertia. While inertia is generally introduced through a finite particle response time, many processes involve particles with a low response time but a finite particle Reynolds number. In this case, theoretical models are rather sparse, and their validity has never been tested against controlled experiments. This work precisely proposes a careful testing of fiber sedimentation and advection models at finite particle Reynolds number against well-controlled two-dimensional experiments. We show that the slender body limit model has strong limitations at finite aspect ratio and Reynolds number, and we identify the main corrections that need to be incorporated into this basic model by expanding on the work of Khayat and Cox [J. Fluid Mech. 209, 435 (1989)]. Additionally, we present the different models under a uniform framework, providing a simpler and clearer use. Using the validated inertial model, we show the importance of the ratio between the settling speed and the typical flow velocity for describing the fiber motion.