The infiltrative nature of malignant gliomas results in active tumor spreading into the peritumoral edema, which is not visible in conventional magnetic resonance imaging (cMRI) even after contrast injection. MR relaxometry (qMRI) measures relaxation rates dependent on tissue properties, and can offer additional contrast mechanisms to highlight the non-enhancing infiltrative tumor. To investigate if qMRI data provides additional information compared to cMRI sequences when considering deep learning-based brain tumor detection and segmentation, preoperative conventional (T1-w per- and post-contrast, T2-w and FLAIR) and quantitative (pre- and post-contrast R1, R2 and proton density) MR data was obtained from 23 patients with typical radiological findings suggestive of a high-grade malignant glioma. 2D deep learning models were trained on transversal slices (n=528) for tumor detection and segmentation using either conventional or quantitative data. Moreover, trends in quantitative R1 and R2 rates of regions identified as relevant for tumor detection by model explainability methods were qualitatively analyzed. Tumor detection and segmentation performance for models trained with a combination of qMRI pre- and post-contrast was the highest (detection MCC=0.72, segmentation DSC=0.90), however, the difference compared to cMRI was not statistically significant. Overall analysis of the relevant regions identified using model explainability showed no differences between models trained on cMRI or qMRI. When looking at the individual cases, relaxation rates of brain regions outside the annotation and identified as relevant for tumor detection exhibited changes after contrast injection similar to region inside the annotation in the majority of cases. In conclusion, models trained on qMRI data obtained similar detection and segmentation performance to those trained on cMRI data, with the advantage of quantitatively measuring brain tissue properties within similar scan time. When considering individual patients, the analysis of relaxation rates of regions identified by model explainability suggests the presence of infiltrative tumor outside the tumor cMRI-based annotation.