If you are concerned that tablets provide learners an inferior reading experience you might be interested in this Educause article. The article outlines a study conducted at the Coast Guard Academy, but also offers an introduction that reviews the existing literature on the topic.
I regard this as a multi-level question. There is the question of reading behaviors as they might exist in the “real world”. There is also the question of reading under controlled circumstances. Reading in the real world involves additional factors that go beyond the basic question of whether comprehension is influenced by whether text is accessed from paper or a tablet. In the real world, it appears that factors such as attractive distractions or display format may impact the reading experience. These issues have practical significance, but can be potentially addressed via technological means. For example, the larger IPad pro will allow more complex page presentations. The reason Kindle text is unadorned is partly to control cost. Access to other apps on an iPad can presently be controlled if distraction is an issue. Tools for deep reading (highlighting, navigation, etc.) will improve.
The bare bones comparison of reading from different displays seems quite different. I can think of no reason I would expect the display type to make a difference, but I guess this is an empirical question. The study reported in this article describes an experiment (and references others) addressing this basic question. The study found no treatment differences (but also reached what I thought were strange conclusions related to the pattern of scores associated with each treatment). The pattern finding and interpretation seem a bit of a stretch. The author suggests that paper may be suited to more capable learners. The data on which this proposal is made would also then encourage the conclusion that more average learners should use tablets.
If you care interested, you can view my Highly highlights associated with this article. I describe Highly elsewhere.