The intermittent damage evolution preceding the failure of heterogeneous brittle solids is well-described by scaling laws. In deciphering their origins, failure is routinely interpreted as a critical transition. However, at odds with expectations of universality, a large scatter in the value of the scaling exponents is reported during acoustic emission experiments. Here we numerically examine the precursory damage activity to reconcile the experimental observations with critical phenomena framework. Along with disorder, we consider an additional parameter that describes the progressive damageability of material elements at mesoscopic scale. This hardening behavior encapsulates the micro-fracturing processes taking place at lower length scales. We find that damage hardening can not only delay the final failure, but also affect the precursory damage activity. For large hardening, the long-range elastic interactions prevail over disorder, ensuring a nearly homogeneous damage evolution before failure that takes place through damage localization, a standard instability. Damage bursts observed prior localization are then reminiscent of depinning transition. On the contrary, when hardening is low, precursors that are still described by scaling laws, are a signature of percolation. The existence of two classes is highlighted by the different values of the exponent characterizing the divergence of the precursor size on approaching failure. Our findings shed new light on the connection between the level of quasi-brittleness of materials and the statistical features of the failure precursors. Finally, they provide a more complete description of the acoustic precursors and thus pave the way for quantitative techniques of damage monitoring of structures-in-service.