I think that there is somewhat of a biophysics question here but it is perhaps buried.
In theory there is no contrast difference, but in practice...
If you are designing for contrast in particular, there is almost no sense in which light-on-dark and dark-on-light can be properly distinguished in the abstract. Like, if "black" and "white" are consistently defined between the two situations, there is no difference between a smattering of white light inside of a black field of view and a smattering of black space inside of a white field of view: the difference between black and white is exactly the same and the contrast difference is zero.
But in practice with contrast, one needs to look at the deep particulars of the two solutions: blackboards are frequently dark grey rather than black and their chalk is often off-white and only deposited in a thin layer, whereas whiteboards are more often really white and a dry-erase marker that is not running out can be nearly black: the contrast is greater on most whiteboards. (On the other hand, the reason that some of us are apparently plagued with dry-erase markers running out on us, is that we like to write high-up with our pens angled upwards, in which case gravity is pulling the ink away from the writing tip into the back of the pen, which is simply not an issue with chalk: if it touches the surface it can write on it.)
Similarly both chalkboards and dry-erase boards lose contrast due to “ghosts” of previous marks sticking around, but this problem is somewhat more of a problem in practice with chalkboards as the chalk is a much more nonreactive substance than the alcohol-affiliated ink.
Some other features of biology also matter
Interestingly, you speak as if contrast is an absolute good but I am not sure that it is. It may be that humans prefer the lower contrast to the higher contrast and that this is why you preferred the blackboards of your youth. I am not sure. Once we get into visual perception I think most of the physics in the situation is gone; I for example find it really hard at night to read signs that are written in glowing blue letters but I cannot easily explain this as a consequence of the physics of blue light. But there are two physics effects that I think are more universal and still matter for the larger consideration.
The first is hysteresis, the fact that your eyes are not coming to the situation from a completely blank context, but rather they are immersed in that context and constantly switching back to it, so that the surroundings matter a lot. In a bright room with white walls, a whiteboard will have less contrast with its surroundings. Conversely if you are giving a presentation in a room where the lights have been turned out, white-on-black presentation is going to reduce eye strain as people look up from your presentation and then back down to you. Probably this is the most important effect.
The second is depth of field, the fact that a brighter context will cause your pupil to contract. As long as we are not illuminating things with the brightness of direct sunlight, your pupil should be able to adjust painlessly to any particular context; the pupil’s contraction is not directly an issue. However a contracted pupil can keep more in focus than a dilated pupil can, with less work for the lens: photographers say that narrower apertures have a greater depth of field. This is why it is harder to take a sharp photograph at night. In a way this also improves contrast; blurring leads to some muddling of contrast around the edges of a letter or the thinnest strokes and dots. So at the same definitions of black and white, there should exist text at a size and distance which is too small to read in the white-on-black configuration (your pupil is just too dilated to help your lens to fully resolve the details) but quite legible in the black-on-white configuration (where your pupil is contracted).