We describe the STANFORD-PARIS and PARIS-STANFORD submissions to the 2017 Extrinsic Parser Evaluation (EPE) Shared Task. The purpose of this shared task was to evaluate dependency graphs on three downstream tasks. Through our submissions, we evaluated the usability of several representations derived from English Universal Dependencies (UD), as well as the Stanford Dependencies (SD), Predicate Argument Structure (PAS), and DM representations. We further compared two parsing strategies: Directly parsing to graph-based dependency representations and a two-stage process of first parsing to surface syntax trees and then applying rule-based augmentations to obtain the final graphs. Overall, our systems performed very well and our submissions ranked first and third. In our analysis, we find that the two-stage parsing process leads to better downstream performance, and that enhanced UD, a graph-based representation, consistently outperforms basic UD, a strict surface syntax representation, suggesting an advantage of enriched representations for downstream tasks.