Dear student,
The better is the nucleophile, the more is its reactivity towards SN2 reaction.
In methoxy group, oxygen is attached to the methyl group which shows +I effect and hence making oxygen more nucleophilic by making it more negative.
In Acetate group, oxygen is attached to a carbonyl carbon which shows -I effect and hence making oxygen less nucleophilic.
Thus, methoxy group is more reactive towards SN2 reaction.
Regards