Running, especially when heavy or overweight puts a lot of stress on your joints, most notably the knees. The effect is worse when you're untrained and don't have a proper technique. Swimming does not, since your body weight is suspended by the water.
"There are caveats, though, especially for people who have suffered significant knee injury or are overweight."
Sure, in moderation it's a small net gain, but few are the correct weight, without injury, and run in moderation.
Note: Simply being tall can have the same effect as being overweight and shorter. The knee supports 3d volume on a 2d surface so it has scaling issues. There is a significant peak load difference between a 5'2" runner and a 6'2" runner.
Edit: "We know from many long-term studies that running doesn't appear to cause much damage to the knees," vs. "In one study, Swedish researchers found that exercise, including jogging, may even be beneficial." So, at best "if you have a relatively normal knee and you're jogging five to six times a week at a moderate pace, then there's every reason to believe that your joints will remain healthy." Which is hardly the same things as saying running is not harmful.
"Is there a causal relationship between running and osteoarthritis? The current data are based on small studies, and their results are often unclear."
I've previously come across the cited studies by Lane, "at 9-year follow-up, the results were the same; there was no difference in the incidence and progression of knee and hip osteoarthritis in runners and nonrunners", but had not seen Sohn's comparison of college varsity runners and swimmers, "There is no association between moderate longdistance running and the future development of osteoarthritis. Furthermore, the evidence suggests that neither heavy mileage nor the number of years running are contributory to the future development of osteoarthritis."
On the other hand, Schmitt et al found that "Osteoarthritis of the knee joint is rare in former elite marathon runners. The risk of osteoarthritis of the hip joint seems to be higher than in control subjects who do not engage in much sport."
"The current evidence in persons who participate in elite sports activity, particularly in sporting groups susceptible to joint injury, suggests that these groups are at increased risk for OA as a result of their participation, but it is unclear whether participation in the absence of injury is harmful. "
Weight and other health issues are a massive and hard to control for Confounding variable in most of these studies. Osteoarthritis causes (weight, injury, bone misalignments etc.) are also likely to inhibit running. At the same time running increases the risk of injury.
Note: Most of these studies are also talking about jogging not running as running is shown to cause damage.
However, from your link "Researchers22 found a significantly higher incidence of osteoarthritis in men (aged 20–49 years) who were involved in high levels of physical activity (ie, walking or running more than 20 miles per week). "
It messes with your knees and heel. When you take a step during a run, your leg lands with your entire body slamming into it.
There are ways to run that are less damaging (better equipment, like socks and shoes, or using the technique where you largely only make contact using the balls of your feet), but it doesn't change the fact of a shock happening.
That said, it's unlikely to be so damaging to you as to outweigh its benefits. Swimming is better mostly because water has less resistance than the ground, and pushing off isn't really a shock to anything.
I looked into this quite a bit some years ago and found no research to suggest more cushioned shoes, less cushioned shoes, pronation-control shoes, barefoot running, etc. have any effect on injury rates. Are there recent studies or info that I missed on this topic?
> it's unlikely to be so damaging to you as to outweigh its benefits
It's even possible that all the shock and load bearing of running /is/ a benefit.
Running is associated with acute injuries of all sorts, but as others have commented does not correlate with osteoarthritis or other long term injuries.