A nonasymptotic performance comparison is presented between the MIN-NORM and MUSIC algorithms for estimating the directions of arrival of narrowband plane waves impinging on an array of sensors. The analysis is based on a finite amount of sensor data. The analysis makes the assumption of high SNR, and it applies to arrays of arbitrary geometry. It is shown that MIN-NORM can be expressed as a certain data-dependent weighted MUSIC algorithm, and that this relationship allows a unified performance comparison. It is also shown that the variances of the estimated directions-of-arrival from the MUSIC algorithm are always smaller than those of the MIN-NORM algorithm at high SNR when both algorithms employ a numerical search procedure to obtain the estimates.