let me start with nucleophilicity of halides. In protic polar solvent, $\ce{F^-}$ is more solvated (hydrogen bonding) than $\ce{I^-}$ and hence less reactive.
In polar aprotic solvent$\ce{F^-}$ solvation is less and therefore more reactive.
Such behavior may not be applicable here, since phenoxide is resonance stabilized while other compound is not. Therefore phenoxide $\bf{2}$ is less nucleophilic than cyclohexanoate $\bf{1}$.
