This paper examines asymptotic performance of MUSIClike algorithms for estimating directions of arrival (DOA) of narrowband complex non-circular sources. Using closedform expressions of the covariance of the asymptotic distribution of different projection matrices, it provides a unifying framework for investigating the asymptotic performance of arbitrary subspace-based algorithms valid for Gaussian or non Gaussian and complex circular or non-circular sources. We also derive different robustness properties from the asymptotic covariance of the estimated DOA given by such algorithms. These results are successively applied to four algorithms: to two attractive MUSIC-like algorithms previously introduced in the literature, to an extension of these algorithms, and to an optimally weighted MUSIC algorithm proposed in this paper. Numerical examples illustrate the performance of the studied algorithms compared to the asymptotically minimum variance (AMV) algorithms introduced as benchmarks.