Direct dependency parsing of the speech signal -- as opposed to parsing speech transcriptions -- has recently been proposed as a task (Pupier et al. 2022), as a way of incorporating prosodic information in the parsing system and bypassing the limitations of a pipeline approach that would consist of using first an Automatic Speech Recognition (ASR) system and then a syntactic parser. In this article, we report on a set of experiments aiming at assessing the performance of two parsing paradigms (graph-based parsing and sequence labeling based parsing) on speech parsing. We perform this evaluation on a large treebank of spoken French, featuring realistic spontaneous conversations. Our findings show that (i) the graph based approach obtain better results across the board (ii) parsing directly from speech outperforms a pipeline approach, despite having 30% fewer parameters.