Background: Metal artifacts arising around high-density components are a widely known problem in X-ray computed tomography (XCT) for both medical and industrial applications. Although phase contrast imaging XCT (PCI-XCT) is known to be less prone to metal artifacts caused by beam hardening, so far only little effort was made for its comparison to other, more established methods. Objective: In the course of this work, this absence in literature is addressed by a quantitative comparison of PCI-XCT to attenuation contrast XCT (AC-XCT). Methods: A polymer specimen including four Ti6Al4V inserts was investigated by PCI- and AC-XCT with different pre-filter settings and metal artifact reduction (MAR) algorithm. Artifacts and image quality were evaluated by a streak index which provides a quantitative metric for the assessment of streak artifacts and contrast-to-noise ratio (CNR). Results: Results showed that streak artifacts are significantly reduced in PCI-XCT and only matched by AC-XCT in combination with hardware pre-filtering of the X-ray beam and post-processing by a MAR algorithm. However, hardware pre-filtering leads to worse CNR and artifacts close to the surface of metal inserts could not be removed sufficiently by the MAR algorithm. Conclusions: This work demonstrates the potential of PCI-XCT for the reduction of metal artifacts and presents the first quantitative comparison to established AC-XCT methods.