I've done both Ibuprofen 400x3 and naproxen 500x2 daily for knee problems, and would say the pain reduction from Ibuprofen is much greater than Naproxen. So much so, that I would say its not a fair comparison, particularly at 600x3.
Tacking on more anecdotal information, I'm a chronic pain sufferer and I've taken every OTC and several prescription NSAIDs at various points over the decades... in my case, ibuprofen was not only harsher on my stomach (roughly as bad as diclofenac), it helped less with pain even at huge doses - it helped more with tension and strangely was better at tooth pain, but far less with my particular joint and muscle pains.
I would have guessed similar to the article - Naproxen was the softest on my stomach for as long as I could take it, but over the years I both built a tolerance for it and it wasn't strong enough so I switched to meloxicam (the gentlest on my stomach and the strongest pain reliever of the group, but only available by prescription) and was on it for nearly a decade. I'd go back on it too if I were able - it was definitely the best thing I've ever taken for my pain. Celecoxib was just more expensive ($20 copay vs $4 generic) and didn't work as well. I'm very sad that NSAIDs are no longer an option for me, as they both reduced the pain and treated it, but unsurprisingly 20 years of taking NSAIDs daily caught up with me... medicine still hasn't come up with a better solution for long term pain management, despite the desperate need.
They are different pain medicines and mileage varies with the person and type of pain you have - and sometimes, your preconceived notions. (some folks have brand biases and so on).
I react well to both of them. Since ibuprofen is cheaper, I am more likely to use it. Though honestly, for my worst recurring pain, I take both ibuprofen and paracet (Tylenol), on advice from the doctor. The same seems to help my spouse with dental pain.
The idea is that it acts as an irritant which increases blood flow and other healing responses to that area. Tendons in particular are thought to heal slowly because they don't have great blood flow. This strikes me as similar to the ideas of dry-needling and platelet-rich plasma injections.
