Plasmonic nanoresonators consisting of a gold nanorod and a spherical silica core and gold shell, both coated with a gain layer, were optimized to maximize the stimulated emission in the near-field (NF-c-type) and the outcoupling into the far-field (FF-c-type) and to enter into the spasing operation region (NF-c*-type). It was shown that in the case of a moderate dye concentration, the nanorod has more advantages: smaller lasing threshold and larger slope efficiency and larger achieved intensities in the near-field in addition to FF-c-type systems’ smaller gain and outflow threshold, earlier dip-to-peak switching in the spectrum and slightly larger far-field outcoupling efficiency. However, the near-field (far-field) bandwidth is smaller for NF-c-type (FF-c-type) core–shell nanoresonators. In the case of a larger dye concentration (NF-c*-type), although the slope efficiency and near-field intensity remain larger for the nanorod, the core–shell nanoresonator is more advantageous, considering the smaller lasing, outflow, absorption and extinction cross-section thresholds and near-field bandwidth as well as the significantly larger internal and external quantum efficiencies. It was also shown that the strong-coupling of time-competing plasmonic modes accompanies the transition from lasing to spasing occurring, when the extinction cross-section crosses zero. As a result of the most efficient enhancement in the forward direction, the most uniform far-field distribution was achieved.