Samir Okasha wrote a rather flawed book on group selection some years ago. However, this article shows that he is doing a good job of keeping up with developments in the field - and it isn't so easy to find significant mistakes in this large recent article.
I think one problem is that it takes the work of Nowak and Wilson a bit too seriously.
In one place the authors argue against equivalence, saying:
In one respect, the kin selection approach is arguably more general than the multilevel approach, because the latter requires that individuals be nested into nonoverlapping groups, as in figure 4; this is necessary for the decomposition technique in box 2 to apply (Hamilton 1975, Okasha 2006, Frank 2013). Groups of this sort exist in some taxa (e.g., the colonies of many social insect species). But in other cases, individuals engage in social interactions with their conspecifics, but there are no well-defined, discrete groups. The kin selection approach can handle such cases easily; indicative of this is that in deriving equation 4 above (box 1), we did not make use of the fact that the individuals were nested into nonoverlapping groups. Therfore, the claim that kin and multilevel selection are formally equivalent requires at least this qualification.
This doesn't seem like too much of a stumbling block to me. The modern "group selection" approaches depend critically on defining a "group" to include any collection of organisms - no matter how fleeting or ephemeral. You have to buy into this conception of a "group" for the approach to be worth considering in the first place.
The authors say:
The widespread preference for kin selection may be partly due to multilevel selection's association with the flawed good-of-the-group tradition of the 1950s and 1960s and the associated superorganism concept, of which many biologists remain suspicious. It is undeniable that the careless appeal to group-level advantage as a way of explaining a trait's evolution led to serious errors in the past, so biologists’ wariness of this mode of explanation is understandable.
That's about the size of it. However, this paints group selection's problems as being in the past. I think that this is inaccurate. A fairly cursory look at the evolutionary social sciences shows that misapplication of group selection is still widespread.
The essay closes with a plea for "causal aptness": use kin selection when you have relatives, use group selection when you have interacting groups. This proposal sounds reasonable - but I think it would do little to stem the existing misuse of group selection. The problem is that people see differential group reproduction, reach for group selection, and produce just-so stories about how group traits are the product of differential group extinction or reproduction. This is a systematically bad methodology that use of group selection directly encourages. Using "causal aptness" would probably boost usage of group selection. That seems as though it is likely to cause a range of negative outcomes associated with the misuse of group selection - and so I regard the proposal as suspect.
"Causal aptness" is one proposal. A big health warning relating to the misuses of group selection is another. I think that, if you adopt the first proposal, you should also adopt the second one.