Flip-chip truncated-pyramid-shaped blue micro-light-emitting diodes (μ-LEDs), with different inclinations of the mesa facets to the epitaxial layer plane, are studied by simulations, implementing experimental information on temperature-dependent parameters and characteristics of large-size devices. Strong non-monotonous dependence of light extraction efficiency (LEE) on the inclination angle is revealed, affecting, remarkably, the overall emission efficiency. Without texturing of emitting surfaces, LEE to air up to 54.4% is predicted for optimized shape of the μ-LED dice, which is higher than that of conventional large-size LEDs. The major factors limiting the μ-LED performance are identified, among which, the most critical are the optical losses originated from incomplete light reflection from metallic electrodes and the high p-contact resistance caused by its small area. Optimization of the p-electrode dimensions enables further improvement of high-current wall-plug efficiency of the devices. The roles of surface recombination, device self-heating, current crowding, and efficiency droop at high current densities, in limitation of the μ-LED efficiency, are assessed. A novel approach implementing the characterization data of large-size LED as the input information for simulations is tested successfully