Over the last fifteen years, ferroelectric (FE) and antiferroelectric (AFE) ultra-thin films based on fluorite-structured materials have drawn significant attention for a wide variety of applications requiring high integration density. AFE ZrO2, in particular, holds significant promise for nanosupercapacitors, owing to its potential for high energy storage density (ESD) and high efficiency (η). This work assesses the potential of high-performance Hf1−xZrxO2 thin films encapsulated by TiN electrodes that show linear dielectric (LD), FE, and AFE behavior. A wake-up effect is observed for AFE ZrO2, a phenomenon barely reported for pure zirconium oxide and AFE materials in general, correlated with the disappearance of the pinched hysteresis loop commonly observed for Zr-doped HfO2 thin films. ESD and η are compared for FE, AFE, and LD samples at the same electrical field (3.5 MV/cm). As expected, ESD is higher for the FE sample (95 J/cm3), but η is ridiculously small (≈55%) because of the opening of the FE hysteresis curve, inducing high loss. Conversely, LD samples exhibit the highest efficiency (nearly 100%), at the expense of a lower ESD. AFE ZrO2 thin film strikes a balance between FE and LD behavior, showing reduced losses compared to the FE sample but an ESD as high as 52 J/cm3 at 3.5 MV/cm. This value can be further increased up to 84 J/cm3 at a higher electrical field (4.0 MV/cm), with an η of 75%, among the highest values reported for fluorite-structured materials, offering promising perspectives for future optimization.