The purpose of this article is to present a comparative study of sparse greedy algorithms that were separately introduced in speech and audio research communities. It is particularly shown that the Matching Pursuit (MP) family of algorithms (MP, OMP, and OOMP) are equivalent to multi-stage gain-shape vector quantization algorithms previously designed for speech signals coding. These algorithms are comparatively evaluated and their merits in terms of trade-off between complexity and performances are discussed. This article is completed by the introduction of the novel methods that take their inspiration from this unified view and recent study in audio sparse decomposition.