Which scientific article has a greater impact, the one that is more frequently cited, or the one that is more frequently read ? The answer is far from trivial, but it seems reasonable that both measures should give an indication of the influence of a published piece of scholarly work. At the present time, however, that importance is quantitatively assessed exclusively through the number of citations that the article garners over time.
This is because a) determining how many people actually read an article was essentially impossible a proposition until not so many years ago, whereas the number of citations is (relatively) easily countable b) the underlying assumption is that a scientist citing a published article has presumably read it, an assumption often questionable, as argued in a recent study.
Do the two things, namely reading and citing, necessarily go together ? Maybe, or maybe not. There is no question, however, that measuring the readership of an article seems much more feasible nowadays, as essentially all scientific journals, as well as ArXiv, maintain online repositories of articles and keep track of things such as article hits and downloads. While these two numbers still do not necessarily measure directly readership , they should reasonably be expected to correlate fairly closely with it. In other words, it is another measure which, while imperfect, ought to have some usefulness.
This immediately raises the question of correlation between readership, as assessed through the procedure suggested above, and number of citations. If, hypothetically, the two things did not go together, i.e., many articles that are widely cited are not equally extensively read, and vice versa articles that are downloaded and read by many end up cited only seldom for a variety of possible (legitimate and illegitimate) reasons, then which papers should be deemed to have had the greater impact ? 
And, along the same lines, is the journal that is most prestigious the one that is most widely read, or rather that with the most cited articles, should the two things not necessarily go together ?
 I for one frequently download the same article several times, just because I have the tendency of purging files ruthlessly, thereby deleting material which I should keep instead.
 For example, let us consider the case of a novel idea that first appears in a manuscript that is extensively cited, but is illustrated more accessibly and clearly on a subsequent manuscript (perhaps by other authors), not equally cited but from which most scientist end up learning about that idea.