The Klein-Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, Vv+V s=constant. These intrinsically relativistic and isospectral problems are solved in the case of squared hyperbolic potential functions and bound states for either particles or antiparticles are found. The eigenvalues and eigenfuntions are discussed in some detail and the effective Compton wavelength is revealed to be an important physical quantity. It is revealed that a boson is better localized than a fermion when they have the same mass and are subjected to the same potentials. © 2008 The Royal Swedish Academy of Sciences.