  In this work we compare mass spectra and decay constants obtained from two
recent, independent, and fully relativistic approaches to the quarkonium
bound-state problem: the Hamiltonian basis light-front quantization (BLFQ)
approach, where light-front wave functions are naturally formulated; and, the
covariant spectator theory (CST), based on a reorganization of the
Bethe-Salpeter equation. Even though conceptually different, both solutions are
obtained in Minkowski space. Comparisons of decay constants for more than ten
states of charmonium and bottomonium show favorable agreement between the two
approaches as well as with experiment where available. We also apply the
Brodsky-Huang-Lepage prescription to convert the CST amplitudes into functions
of light-front variables. This provides an ideal opportunity to investigate the
similarities and differences at the level of the wave functions. Several
qualitative features are observed in remarkable agreement between the two
approaches even for the rarely addressed excited states. Leading twist
distribution amplitudes as well as parton distribution functions of heavy
quarkonia are also analyzed.
