Yep, there are no good experimental designs for breastmilk that are also ethically ok.

What is really interesting about this study is that it is based on a a cohort of pre-term babies in randomised and blinded study from the 1980s [1] - where they randomised between formula and donor breast milk. You can read the conclusions easily from the link, but essentially the donor breast milk fed babies did far worse than the formula fed ones, both overall and in subset analysis. Their conclusion is that preterm babies are in need of adequate nutrition, and, reading between the lines, donor breast milk does not provide this.

Where the paper gets confusing is when we start to look at the analysis of the mother's breast milk, which occurred in a follow-up study in the 90s [2]. Of course, this was not randomised, and was parental choice. The 90s paper showed a significantly higher IQ in those fed with mother's breast milk. I say this is confusing because the later papers mention that the trial is randomised (the result of which showed a negative effect for breast milk, albeit donor), while they are actually comparing two groups in an observational study (mother's breast milk vs not).

So actually, we go back to the usual 'can we correct for everything' in an observational study? We should be very cautious drawing conclusions from observational studies - there are nice examples of these studies showing the exact opposite of the randomised study - for example in this trial which set out to show anti-oxidants prevented cancer [3], they managed to show simultaneously that the obversational findings directly contradicted the randomised findings.

A better study is the cluster-randomised study [4] in Belarus, but even this study has many flaws - it was cluster-randomised, those randomised to receive teaching on the benefits of breast milk also received a lot more input and support from their midwives and hospitals in general. There was a significant difference in IQ between groups, though the measurement was not blinded. There was a trend, but no significance in the difference between teachers rating of the groups.

Another study looking at sibling pairs didn't find a difference between siblings who had and hadn't been breastfed - this is still an observational study, but being siblings it controls for a few more things. [5]

Anyway, there are lots of issues in breast-feeding research. Another is comparing 1st to 3rd world, where other issues, particularly infection risk becomes important. Formula milk contains iron, which is pretty important in cognitive development. Breast milk does not contain any. This may have been an evolved mechanism to protect from infections, given that (almost) all infections require ready access to iron, and may explain the increased risk of serious infections in 3rd world countries.

To sum up, I don't personally believe there is good enough evidence to recommend breast feeding over formula feeding. For a parent it should come down to individual situations. Our first child was slightly micrognathic, which made breast feeding very painful. In retrospect we pursued breast feeding for far too long, and it was causing stress in both mother and child, which I doubt is beneficial to psychological health. Our second kid would only take breast and was easy to feed. Our third took breast without a problem, but was left hungry so needed topped up with formula.

[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1792630/
[2] https://www.ncbi.nlm.nih.gov/pubmed/1346280
[3] https://www.ncbi.nlm.nih.gov/pubmed/8127329
[4] https://www.ncbi.nlm.nih.gov/pubmed/18458209
[5] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1633819/