Intensive tillage (CT) application in Mediterranean olive orchards has threatened soil quality and led to soil degradation. No tillage with bare soil (NT+H) has been considered as an alternative practice to this management system; however, there are discrepancies in the literature on the results of the application of this practice. Our main objective was to assess the impact of continuous tillage and zero tillage on soil aggregate stability, SOC and SON stocks. The study was conducted in a Mediterranean rainfed olive grove under semi-arid conditions in a Calcaric Cambisol, for 16 years evaluating complete soil profiles (0–120 cm depth). In the long-term, the management practices CT1 and NT+H significantly affected aggregate particle size by reducing the percentage of macro-aggregates (>250 μm) and promoting a higher number of micro-aggregates (<250 μm). Nevertheless, NT+H affected the Bw and BC horizons with the increase in the large macroaggregates (>2000 μm) percentage. In relation to these results, the soil structural stability indices showed a significant decrease in both Mean Weight Diameter (MWD) and Geometric Mean Diameter (GMD) values with losses of more than 50% with respect to the initial period (CT0) in the first two horizons. In the long term, both in CT1 and in NT+H, higher SOC concentrations were found in deep horizons showing a C redistribution in depth and important losses in TN values—while, in CT0, macroaggregates contained the highest CPC values, after the long-term both management practices (CT1 and NT+H) affected the C dynamics and were characterised by higher C pool in the microaggregates than in the macroaggregate fractions. Therefore, long-term NT+H and CT1 showed an SOC storage deterioration and increased susceptibility to decomposition, CO2 emissions and fertility losses. This trend i.e., decreases in SOC stocks following NT, confirms previous studies on the subject and points to nutrient balance impacts.