This work presents a direct comparison between classical three-dimensional (3D) elasticity solid finite elements (FEs) and high-order one-dimensional (1D) beam theories developed within the Carrera Unified Formulation (CUF). Although solid elements are widely adopted as the reference modelling strategy in structural mechanics, they exhibit significant limitations: aspect-ratio sensitivity, mesh and mode dependency, and the need for highly refined discretizations. These issues often lead to locking phenomena, poor convergence, and significant challenges when analyzing thin-walled, slender, or composite structures. To overcome these limitations, this study employs higher-fidelity 1D beam elements with full 3D capabilities. Instead of relying on full 3D elasticity formulations, it is shown that comparable accuracy can be achieved through refined 1D structural theories. These models, derived directly from 3D elasticity, reproduce the solid response while dramatically reducing computational cost. Within the CUF, higher-order beam theories are systematically developed through a unified index-based notation, enabling the straightforward construction of refined models. The key idea of CUF is the introduction of expansion functions, in addition to standard FE interpolation functions, to enrich the kinematic description of the beam cross-section. This allows capturing essential 3D effects, including torsion-bending coupling, warping, and cross-sectional deformation. Stress and free-vibration analyses of isotropic and composite compact or thin-walled structures are presented to highlight the performance of CUF 1D models against classical 3D solid FEs. Particular attention is devoted to mesh sensitivity, mode dependency, and computational efficiency, especially for accurate 3D stress distributions or higher vibration modes evaluation where solid elements typically require substantial refinement to converge. The results demonstrate that CUF high-order beam theories offer robust and efficient alternatives to traditional solid elements. By combining accuracy, reduced computational effort, and insensitivity to element aspect ratio or mode dependency, these refined 1D models provide a powerful modelling strategy for parametric studies, optimization frameworks, and the analysis of next-generation structures.