I was at their office and tested reMarkable a bit. The delay is surprisingly low. If i did quick circle shapes over the display the pen would be 5-8 cm in front of the line. When writing normally i didn't feel or notice any lag at all really. The display itself is also more rugged then a kindle paperwhite, so writing gives enough resistance to feel "paper-ish". The software does a correction after writing, so ragged shapes gets smoothed out and i saw some fills being added. I'm unsure how much of this is being tested and tweaked.
What is happening is that a light grey shadow appears very fast, and then the ink "fills in" fluidly until achieving its final dark grey. The effect is like some "magic ink" that dries in contact with air. It's not exactly like pen and paper, but they've achieved an effect that psychologically works well for me.
The Sony epad [1] seems to be right there in terms of writing speed, if we can trust either video.
Put their video[1] in 0.25x slow motion and watch at 39 seconds, the 's' they write at the end of 'Restrictions', see it gets the start and end missed and the shape distorted. Then watch the filling in sketching movements at 40 seconds, the ink appearing lags by the entire length of the pen stroke...
Yet in a couple of places, it looks like it is keeping up with writing. Where they say it's the fastest, where they zoom in on his handwriting.
I want it to be paper. But ... I dunno...
[1] https://youtu.be/34I27KPZM6g?t=38