Nonlinear discretizations are necessary for convection--diffusion--reaction equations to obtain accurate solutions that satisfy the discrete maximum principle (DMP). Algebraic stabilization methods belong to a small class of finite element discretizations that satisfy this property \cite{BJK25}. In this talk, we extend a residual-based \emph{a posteriori} error estimation framework, originally developed for algebraic flux correction (AFC) schemes \cite{Jha21}, to recently proposed algebraic stabilization schemes \cite{Jha24}. The performance of the methods is assessed in terms of accuracy, such as the smearing of layers, as well as efficiency in solving the associated nonlinear problems. The results indicate that algebraic stabilization methods are significantly more efficient than AFC schemes while achieving the same order of accuracy.