I'm jumping in, because this is something that has confused me for a while. Supposedly, nucleophilicity and basicity are strongly correlated, but they're not the same. Basicity is easy to check through pka values, with strong bases having higher pka values. Nuclephilicity, from my understanding, also takes into account the volume of the nucleophile and the steric effects it might produce in a particular reaction.
In the examples above, the negative charge is more stabilized in CH3COO- than in PhO-, because of the aromaticity of the latter. CH3O- is the better nucleophile because its negative charge is less stabilized (no electron-withdrawing groups other than O and no ressonance possibility, plus the methyl group is electron-donating) and the ion is relatively small. The same logic applies to the nitrogen series.