We derive stellar population parameters for a representative sample of ultracompact dwarfs (UCDs) and a large sample of massive globular clusters (GCs) with stellar masses $gtrsim$ 10$^{6}$ $M_{odot}$ in the central galaxy M87 of the Virgo galaxy cluster, based on model fitting to the Lick-index measurements from both the literature and new observations. After necessary spectral stacking of the relatively faint objects in our initial sample of 40 UCDs and 118 GCs, we obtain 30 sets of Lick-index measurements for UCDs and 80 for GCs. The M87 UCDs have ages $gtrsim$ 8 Gyr and [$alpha$/Fe] $simeq$ 0.4 dex, in agreement with previous studies based on smaller samples. The literature UCDs, located in lower-density environments than M87, extend to younger ages and smaller [$alpha$/Fe] (at given metallicities) than M87 UCDs, resembling the environmental dependence of the Virgo dE nuclei. The UCDs exhibit a positive mass-metallicity relation (MZR), which flattens and connects compact ellipticals at stellar masses $gtrsim$ 10$^{8}$ $M_{odot}$. The Virgo dE nuclei largely follow the average MZR of UCDs, whereas most of the M87 GCs are offset towards higher metallicities for given stellar masses. The difference between the mass-metallicity distributions of UCDs and GCs may be qualitatively understood as a result of their different physical sizes at birth in a self-enrichment scenario or of galactic nuclear cluster star formation efficiency being relatively low in a tidal stripping scenario for UCD formation. The existing observations provide the necessary but not sufficient evidence for tidally stripped dE nuclei being the dominant contributors to the M87 UCDs.
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