We study the performance of modal analysis using sparse linear arrays (SLAs) such as nested and co-prime arrays, in both first-order and second-order measurement models. We treat SLAs as constructed from a subset of sensors in a dense uniform linear array (ULA), and characterize the performance loss of SLAs with respect to the ULA due to using much fewer sensors. In particular, we claim that, provided the same aperture, in order to achieve comparable performance in terms of Cramér-Rao bound (CRB) for modal analysis, SLAs require more snapshots, of which the number is about the number of snapshots used by ULA times the compression ratio in the number of sensors. This is shown analytically for the case with one undamped mode, as well as empirically via extensive numerical experiments for more complex scenarios. Moreover, the misspecified CRB proposed by Richmond and Horowitz is also studied, where SLAs suffer more performance loss than their ULA counterpart.