Dialkylation reactions
Both mechanisms will probably be present but $S_N2$ will dominate because the enolate anion is a strong nucleophile. $E2$ will not occur because there are no $\beta$ hydrogens available on the benzyl chloride. Despite the relative stability of the benzyl cation, especially in protic solvents, the strong nature of the enolate nucleophile and the lack of an $E2$ pathway means that $S_N2$ will probably dominate.

For a comparison of alkyl halide reactivities with different nucleophiles, see this link.