I've seen research by Estee Lauder and Perricone, actual clinical research. Several products will show tiny survey results like x% of participants reported looking more radiant, which isn't terribly helpful. I think that if you wanted a real comparison brand to brand, you would have to dive really deeply into things like quarterly reports to shareholders with spending breakdowns, and of course those are only available for publicly traded companies. Your question made me wonder why we aren't given this information more freely, and I can think of two reasons offhand, that it would unintentionally expose just how high profits really are versus the prices we're charged as consumers, and secondly that we would want to see more research results, many of which would sound really negative to the public because there is always a lot of failure before success. I also suspect that in reality, most claims are marketing woo based on general beliefs of what is traditionally believed about certain ingredients. If we sat down and looked at how every penny the vast majority of brands are spent, I strongly suspect that marketing and legal advice on how to thread the needle on marketing laws would vastly outrank actual research expenses.
All of that being said, I have crepey lids as well, and one product that has really delivered results for me is SubQ Skin by Hylamide, which is another brand from the parent company of The Ordinary, Deciem. They also have a specific eye product, SubQ Eyes, which I tried after I was already using the Skin product, so I don't know that it added anything (big disclaimer, I don't have dark circles, which is a big part of their Eye product claims), but I stopped using the Eye product because it was breaking me out, which is rare and I don't think makes it a bad product for other people. Honestly, even if I stopped using SubQ Skin on the rest of my face, I would still buy it just for how much is does to improve the crepiness of my lids ( lol, spell check thinks it improves the creepiness of my kids). I've spent more than a few dollars on eye products, and I don't ever remember anything firming my lids so well. It also really helps that it only costs $22 for an ounce of product. I don't know that you could find a drugstore eye product priced so well.
I don't know any kind of breakdown of what Deciem spends on research, but I do know that they spend it. All of their lines are full of very innovative products, many with ingredients unique to them. I suspect that most real research dollars go into patented ingredients sold wholesale to skincare brands, and much of the meatier performance claims refer to the research done by the companies that developed those ingredients.
By all means, check out Deciem, there is so much more to them than The Ordinary, which is their least expensive facial care line. Hylamide is slightly more expensive and is designed to be a streamlined routine. NIOD is their prestige line with both very innovative and very traditional ingredients influencing their products. Estee Lauder owns a piece of Deciem, but my understanding is that it is a small but influential piece. Beauty business sites will probably have more of the kind of information you're looking for, and there is a fantastic blog by kindofstephen that tracks industry developments.
Wherever your research leads you, I definitely recommend giving Hylamide SubQ Skin a go. I would pay a lot more for it than it costs, especially for my lids!