We present updated constraints on cosmic string and superstring parameters derived from Cosmic Microwave Background (CMB) anisotropies. The constraints are obtained via Markov Chain Monte Carlo (MCMC) analyses of the full temperature and polarization data combined with the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6). For ordinary cosmic strings, we constrain the string tension $G\mu$, the string wiggliness parameter $\alpha$, and the self-chopping efficiency $\tilde{c}$. For cosmic superstrings, we constrain the fundamental string tension $G{\mu }_F$, the string coupling $g_s$, and a parameter $w$ describing the volume of the compact extra dimensions. In both cases, we find significantly tighter bounds on the string tension compared to previous analyses, obtaining $2\sigma$ upper limits of $G\mu <3.66\times {10}^{-8}$ and $G{\mu }_F<1.38\times {10}^{-8}$. We also discuss the significant prior-dependence of these results. The computational pipeline used in this work, including a modified version of capable of computing CMB anisotropies sourced by any active network described via unequal-time correlators, is released publicly as .