To first establish a baseline: Reading is great for your brain, your mind, your intellect. But it can be bad for everything else. You sit, you concentrate, you stress your eyes.
It is such a common causal connection that the NHS simplifies the analysis of causes for myopia down to genes and:
Short-sightedness (myopia) usually occurs when the eyes grow slightly too long, which means they're unable to produce a clear image of objects in the distance.
It's not clear exactly why this happens, but it's thought to be the result of a combination of genetic and environmental factors that disrupt the normal development of the eye.
Too little time outdoors
Research has found that spending time playing outside as a child may reduce your chances of becoming short-sighted, and existing short-sightedness may progress less quickly.
This may be related to light levels outdoors being much brighter than indoors. Both sport and relaxation outdoors appear to be beneficial in reducing the risk of short-sightedness.
Excessive close work
Spending a lot of time focusing your eyes on nearby objects, such as reading, writing and possibly using hand-held devices (phones and tablets) and computers can also increase your risk of developing short-sightedness.
An "everything in moderation" approach is therefore generally recommended. Although children should be encouraged to read, they should also spend some time away from reading and computer games each day doing outdoor activities.
NHS: Short-sightedness (myopia), Causes (2015)
"Too little time outdoors" is a shortcut for expressing giving the muscles and lenses of your eyes a workout with natural variation. Outdoors you usually have to focus objects that vary quite a bit in terms of distance etc. The evidence is slowly coming in for interventions regarding these stresses to improve things:
A stronger effect was found at a school in southern Taiwan, where teachers were asked to send children outside for all 80 minutes of their daily break time instead of giving them the choice to stay inside. After one year, doctors had diagnosed myopia in 8% of the children, compared with 18% at a nearby school
Elie Dolgin: "The Myopia Boom. Short-Sightedness is Reaching Epidemic Proportions. Some Scientists Think they have Found a Reason Why." Nature, Vol. 519, 19 March 2015, 276–278. Also, compare with David L. Ehrlich: "Near Vision Stress: Vergence Adaptation and Accommodative Fatigue", OPO, Volume 7, Issue 4 1987.
Reading on screens is so much worse that its effects got their own term: Computer vision syndrome.
Some decades back, before the advent of computers, the office work involved a range of activities, including typing, filing, reading and writing etc. All these activities are different from each other and needed different types of posture and vision, causing a natural break from each activity. With the computer all these activities were combined and needed no change of posture or vision of the user from his desktop. It certainly improved the quality of the work and efficiency but caused ocular problems, such as dry eye, redness, irritation, eye strain, tired eyes, temporary blurred vision, light sensitivity and muscular problems that stem from using a computer. All these symptoms collectively referred to as computer vision syndrome, which comprised of ocular surface abnormalities or accommodative spasms and/or extra-ocular (ergonomic) aetiologies due to improper posture such as neck and upper back pain and headache.
The major contributors to CVS is thought to be the dry eye, the visual effects of video display terminals (VDT) such as lighting, glare, display quality, refresh rates and radiation and positioning of computer monitors.
Saman Wimalasundera: "Computer vision syndrome", Galle Medical Journal, Vol 11: No. 1, September 2006.
Since now we have Millions at risk of computer vision syndrome it seems quite easy to refer to this simplified risk hierarchy: no reading, paper reading, screen reading. But it should be clear that this problem is indeed one that can be mitigated with adhering to proper ergonomic principles. Apart from the behaviour a user/reader might adapt, such as variation in distance, breaks, body posture, the different sources – or better surfaces – of reading material should be watched out for. A high gloss magazine read on a sunny beach might be quite stressful for the eyes whereas an ergonomic, non-glare, high resolution display might fare quite a bit better.
Significant eye symptoms relate to VDU use often occur and should not be underestimated. The increasing use of electronic devices with flat-panel display should prompt users to take appropriate measures to prevent or to relieve the eye symptoms arising from their use.
Esteban Porcar et al.: "Visual and ocular effects from the use of flat-panel displays", Int J Ophthalmol. 2016; 9(6): 881–885. doi:10.18240/ijo.2016.06.16
While these ergonomics were theoretically known for a long time and the progressivists promised a brighter future (pun intended):
Most people now have some contact with computers either at work or at home. With survey evidence suggesting that perhaps 50% or more of these individ- uals complain of some form of eye problems associ- ated with using computers, eye-care professionals, ergonomists and engineers are faced with a major chal- lenge. Improvements in display technologies continue apace and the next generation of displays will produce images of equivalent quality to typeset hardcopy. Speech recognition and synthesis are already available and this and other technologies are likely to reduce the visual demands of interacting with a computer.
In the meantime, solving the problems of individual users requires a holistic approach, taking account of workstation design, workpractices and psychological factors as well as optometric data.
W.DavidThomson: "Eye problems and visual display terminals—the facts and the fallacies", Ophthalmic and Physiological Optics, Volume 18, Issue 2, March 1998, Pages 111-119
it seems that neither consumers nor some vendors and producers seem to really care. One of the largest manufacturers of displays, in phones, tablets, desktops and laptops has indeed not a single non-glare display on offer. If this is an oversight from the manufacturer, you still should not buy such a rotten fruit if you value your eyesight and have to read from displays.