Viscous and thermal effects occur during the propagation of linear waves in a pipe. Many propagation models are used in musical acoustics, based on different assumptions that induce various model errors. The thermoviscous (or viscothermal) equations are derived from the non-linear 3D Navier-Stokes (NS) equations for a perfect gas by linearization around a uniform steady state. Analytical or numerical solutions can be proposed, after more or less deep modifications of the original system. These derived models will be summarized in a synthetic diagram specifying the assumptions performed for each one. Far from the walls, a standard 3D Helmholtz equation is valid while an effective boundary condition can replace the viscothermal "boundary layers" near the walls of the pipe. Available 1D models describe the propagation of the mean pressure on a well chosen surface and account for thermoviscous effects as a modification of the transmission line coefficients, for cylindrical and conical geometries. This work proposes an evaluation of some of these models (3D and 1D), through a quantitative estimation of model errors in relation to their domains of validity, as well as a numerical comparison for cylindrical and conical domains of propagation.