Bhabha vs. Moeller scattering as a contact-interaction analyzer at a polarized linear collider

We discuss electron-electron contact-interaction searches in the processes e sup + e sup -->e sup + e sup - and e sup - e sup -->e sup - e sup - at planned Linear Colliders run in the e sup + e sup - and e sup - e sup - modes with both beams longitudinally polarized. Our analysis is based on the measurement, for the two processes, of polarized differential cross sections, and allows to simultaneously take into account the general set of electron contact interaction couplings as independent, non-zero, parameters thus avoiding the simplifying choice of a model. We evaluate the corresponding model-independent constraints on the contact coupling constants, emphasizing the role of the available beam polarization and the complementarity, as far as the chirality of the constants is concerned, of the two processes in giving the best constraints. We also make a comparison with the potential of e sup + e sup --> mu supmu sup - at the same energy and initial beams polarization.