We derive self-consistent dimensional (1-D) asymptotic models for fiber flows of liquid crystal polymers using six full 3-dimensional (3-D) approximate BMAB models obtained from different closure approximations to the BMAB kinetic theory. We then evaluate the approximate models by comparing the steady state solutions of the leading order 1-D models to the solutions of the kinetic theory at the flow centerline with boundary conditions consistent with fiber spinning processes. We observe that the solutions of the leading order hydrodynamic variables (axial velocity, pressure and the fiber radius) are insensitive to the choice of the 1-D models and in excellent agreement with the corresponding solutions of the kinetic theory; In particular the order parameter solutions of the DHL2 and DD model, exceeding those of the other approximate models, approximate the corresponding solutions of the kinetic equation very well. At the next order, all the approximate 1-D models predict a radially enhanced inward tilt toward the flow centerline for the flow-aligning director at sufficiently high draw ratios. At the second order, all approximate 1-D models except for the HL11 and HL1D model yield a vanishing biaxial order parameter downstream at sufficiently high draw ratios, suggesting flow-induced uniform uniaxial symmetry within the fiber cross-section. Whereas, the HL11 and HL1D model yield a persistent biaxial symmetry within the fiber cross-section away from the centerline, which we believe to be erroneous. Therefore, for fiber flows, we recommend the DD and DHL2 model.