In this paper we compare two grammar-based generation algorithms: the Semantic-Head-Driven Generation Algorithm (SHDGA), and the Essential Arguments Algorithm (EAA). Both algorithms have successfully addressed several outstanding problems in grammarbased generation, including dealing with non-monotonic compositionality of representation, left-recursion, deadlock-prone rules, and nondeterminism. We concentrate here on the comparison of selected properties: generality, efficiency, and determinism. We show that EAA's traversals of the analysis tree for a given language construct, include also the one taken on by SHDGA. .