In this paper, we determine the efficiency of all commonly occurring eigenvalues-based topological descriptors for measuring the π-electronic energy of lower polycyclic aromatic hydrocarbons. Results show some favorable outcomes as the spectrum-based descriptors such as the adjacency energy, the arithmetic-geometric energy, the geometric-arithmetic energy, and the adjacency Estrada index have the best correlation coefficients greater than 0.999 among all others. However, certain well-known spectrum-based descriptors such as the adjacency, Laplacian & signless Laplacian spectral radii, and the first & second Zagreb Estrada indices show considerably weak performance. Poor performances of the first & second Zagreb Estrada indices are, in general, unexpected. The arithmetic-geometric and geometric-arithmetic energies with correlation coefficients 0.99997 and 0.99996, respectively, are warranted for further use in quantitative structure activity/property relationship (QSAR/QSPR) models. Based on our comparative testing, we generate a priority list of the top five spectrum-based topological descriptors for measuring the π-electronic energy. These best preforming descriptors are then studied for certain infinite families of boron triangular and boron α-nanotubes. The results help in determining the π-electronic energy of these families of boron nanotubes. Combining our results with similar results studied in literature, we conclude that among all the classes of topological descriptors, spectrum-based descriptors are the best in correlating the π-electronic energy.