So apparently Doom 1&2 have the wrong aspect ratio, inferior sound and music compared to the originals and run at 35 FPS like the originals that were made for 70 Hz monitors, but it's an issue for 60 Hz monitors/TVs.
The situation is better for Doom 3, the 4K consoles run at native 4k, PS4, XB1 and Switch at native 1080p, Switch handheld native 720p. All versions target 60 FPS while the Switch version seems to be the only one with drops (and handheld running better than docked). But it's better than the PS3 and 360 versions.
I'm a bit disappointed about 1&2 because they could have made a better job, but considering to get 3 if I feel like playing it on a handheld. Still replaying the original PC version every few years.