p-methoxybenzyl bromide reacts with ethanol faster than p-nitrobenzylbromide because methoxy group at the para position is an electron donating group, and hence increases the electron density on the methyl group at the other end. this makes it easier for the bromo group to react with H+ from ethanol, hence forming an ether.

on the other hand, nitro group at the para position is electron withdrawing, which results in the bromo group being more tightly held to he methyl group and showing low reactivity with ethanol.