Parsing CFLs (simulating PDA vs CYK algorithm)
Wikipedia mentions that the class of deterministic context-free languages can be parsed in linear time, using an LR parser. In contrast, the fastest algorithm for parsing general context-free languages, Valiant's modification of the CYK algorithm, runs in time $O(n^\omega)$ (where $\omega$ is the matrix multiplication constant), and there is evidence due to Lee that any practical implementation of Valiant's algorithm will run in time proportional to $n^{2.43}$ at best (substitute $\epsilon = 3-2.81$ in Lee's paper; here $2.81$ is the exponent of Strassen's algorithm), and in time proportional to $n^3$ for most values of $n$ occurring in practice.

Context-free grammars used in practice tend to be deterministic, precisely because DCFLs can be parsed faster than CFLs. Indeed, even more restricted variants are commonly used (LALR languages) for reasons of efficiency.