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The AC loss performance of two BSCCO and two YBCO conductors of different geometry, characterized by the same self-field critical current of 150 A, is analysed and compared quantitatively. The comparison is made using the finite-element method with a non-linear B-dependent E-J relation. A new shell-region model is utilised for the simulations of thin YBCO strips. Different AC working conditions are simulated: self-field, applied external field, and combined transport current and external perpendicular field application. Magnetic field and current density profiles are investigated in order to illustrate the reasons for the loss difference in the conductors. Depending on the application, the advantages of using BSCCO or YBCO conductors with specific geometry are outlined.