Which set of reactants is better for preparation of 1-methoxy-4-nitrobenzene?
Drastic conditions for reaction 1? Not really. Reflux the reactants in $\ce{MeOH}$ and the reaction should go smoothly and in high yield.

Reaction 2 - two difficulties.
The anion of 4-nitrophenol is very stable and, because of the electron withdrawing power of the nitro group, it is not very nucleophilic. Second difficulty is that bromomethane has a boiling point of 3C so the reaction mixture has to be kept cold to keep it in the reaction mixture. This does not help you overcome the poor nucleophilicity of your phenoxide.

Without running the two reactions it is guesswork to predict which will give the better outcome, but I favour the SNAr.