As far as I could think, the phenoxide ion is comparatively larger as compared to acetate ion, so it should undergo less solvation in presence of a protic solvent and thus its nucleophilicty should be more than that of acetate ion (in a protic medium). This is precisely what my solution sheet says. Also, acetate ion has more dispersed electron density due to it being a much better electron withdrawing group than phenoxide ion, so combining both of these points, phenoxide ion should be a overall better nucleophile than acetate ion. But from here:
acetate ion: In the acetate ion, the methyl group is an electron donating group. The negatively charged oxygen atom increases the electron density around the carbonyl carbon Thus, the acetate ion is more nucleophilic than the phenoxide ion.
From this answer, I do seem to understand that there is always more to nucleophilicity than can be estimated with electronic and size related effects. But still, such questions is frequent in my textbook. I need to understand as how exactly should I compare relative nucleophilicity of given nucleophiles here. Also, if the solvent is changed to a aprotic solvent, would it lead to any difference here?