This paper presents a quantitative comparison of the AC loss performance of two BSCCO and two YBCO conductors, characterized by the same self-field critical current of 150 A. In particular, compared are a 37-filamentary BSCCO tape, a 16-filamentary BSCCO square wire, a standard YBCO tape, and a stack of four narrower YBCO tapes. The comparison is made using a numerical technique, based on the finite-element method, which employs a non-linear E-J relation with the dependence of the critical current density Jc on the local magnetic field. For the simulations of YBCO, a new shell-region model is utilised, which allows overcoming the geometry and mesh problems, typical for superconductors with very high aspect ratio. Different AC working conditions are simulated: self-field, applied external field, and combined transport current and external field of varying orientation. Outlined are the advantages of using BSCCO or YBCO conductors for the different applications. Various magnetic field and current density profiles are investigated in order to illustrate the reasons for the loss difference in the four conductors. Particular attention is drawn to the YBCO tape and the YBCO stack, whose AC loss characteristics are less studied than those of BSCCO conductors.