We conducted a large-scale study of human perceptual quality judgments of High Dynamic Range (HDR) and Standard Dynamic Range (SDR) videos subjected to scaling and compression levels and viewed on three different display devices. While conventional expectations are that HDR quality is better than SDR quality, we have found subject preference of HDR versus SDR depends heavily on the display device, as well as on resolution scaling and bitrate. To study this question, we collected more than 23,000 quality ratings from 67 volunteers who watched 356 videos on OLED, QLED, and LCD televisions, and among many other findings, observed that HDR videos were often rated as lower quality than SDR videos at lower bitrates, particularly when viewed on LCD and QLED displays. Since it is of interest to be able to measure the quality of videos under these scenarios, e.g. to inform decisions regarding scaling, compression, and SDR vs HDR, we tested several well-known full-reference and no-reference video quality models on the new database. Towards advancing progress on this problem, we also developed a novel no-reference model called HDRPatchMAX, that uses a contrast-based analysis of classical and bit-depth features to predict quality more accurately than existing metrics.