A characteristic property of superfluidity and -conductivity is the presence of quantized vortices in rotating systems. To study the BEC-BCS crossover the two most common methods are the Bogoliubov-De Gennes theory and the usage of an effective field theory. In order to simplify the calculations for one vortex, it is often assumed that the hyperbolic tangent yields a good approximation for the vortex structure. The combination of a variational vortex structure, together with cylindrical symmetry yields analytic (or numerically simple) expressions. The focus of this article is to investigate to what extent this analytic fit truly reflects the vortex structure throughout the BEC-BCS crossover at finite temperatures. The vortex structure will be determined using the effective field theory presented in [Eur. Phys. Journal B 88, 122 (2015)] and compared to the variational analytic solution. By doing this it is possible to see where these two structures agree, and where they differ. This comparison results in a range of applicability where the hyperbolic tangent will be a good fit for the vortex structure.