Aggregate price shocks can lead to significant inequality in losses both across and within income groups. This creates a trade-off between supporting households through subsidies, which target those most affected but introduce inefficiencies, and transfers, which are less distortionary but harder to target precisely. We develop a framework to quantify this trade-off, using rich panel data on energy spending and income, alongside price and policy variation from the 2022-23 European Energy Crisis. We show that, in the absence of policy intervention, average household welfare losses would have been equivalent to 6% of income, with some households facing much larger losses. A combination of an energy price subsidy and universal transfers reduced both the mean and dispersion of household losses but incurred efficiency costs equivalent to 12% of the total funds spent on the relief package. Under a range of social preferences, better targeted transfers would have reduced the optimal subsidy rate, though not eliminated it entirely.