I see that Dienekes has provided some analysis of the paper:
http://www.dienekes.blogspot.com/2015/06/into-out-of-and-across-eurasian-steppe.html
It bears close reading, I think.
"The first conclusion of the new study is the detection of the
migration from the steppe to Europe that was the title piece of the earlier study.
The authors do not present quantitative estimates of the amount of demographic replacement effected by the Yamnaya-to-Corded Ware migration, so it will be interesting to see if there are any minor significant differences in these. But, the two papers have different Yamnaya and Corded Ware samples, and yet arrive at qualitatively similar conclusions, so at least this part of the story should be considered firmly "settled"."
"The second conclusion is the migration
from the European steppe to the Afanasievo culture of the Altai... This confirms movement #2 of the Anthony/Ringe
model, although I doubt that this migration had anything to do with Tocharians as detailed below. But, it did happen."
"The third conclusion is that the later steppe cultures of the
Sintashta and Andronovo (putative Indo-Iranians according to some),
were not a continuation of the Yamnaya-Afanasievo people, but had
extra Neolithic farmer ancestry. So, it seems that Neolithic farmers entered the steppe, and the development of steppe cultures did not happen in isolation.
Whether this involved migration of Corded Ware people (as the authors prefer), who were already a mixture of Yamnaya and Neolithic farmers, or some other mixture of Neolithic farmers with steppe populations (e.g., Tripolye plus Yamnaya) remains to be seen."
"As for the Yamnaya, the authors do not find a very strong signal of admixture (as did the earlier study), which they attribute quite plausibly to the lack of eastern hunter-gatherers in their dataset. On the other hand, they claim that the "Caucasus" genetic component in the steppe populations was of steppe ancestry rather than Near Eastern/Caucasian origin as was claimed in the earlier paper. This is based on the statistic
D(Yoruba, Armenia BA; Yamnaya, Corded Ware) that is not significantly different from zero. However, Corded Ware is a mixture of Yamnaya and European Neolithic, so the sign of this statistic is determined by the sign of the statistic
D(Yoruba, Armenia BA; Yamnaya, European Neolithic). If Yamnaya was simply a steppe population, descendants of local people without ancestry from the Middle East/Caucasus, then this statistic would be
positive because of the shared Middle Eastern ancestry of Armenia BA and European Neolithic. Whereas, if Yamnaya is a mixture of a steppe population and a Middle Eastern/Caucasian one, then the statistic would be positive/negative for the respective parts, which would be consistent with an average not different from zero. I am sure that when the new data is re-analyzed together with the eastern hunter-gatherers it will be clear that the Yamnaya are not a pure steppe population."

"Speaking of the Caucasus/Middle East, it seems clear as a first approximation that
the Bronze Age Armenians are quite similar to modern Armenians. Whether the genetic continuity of Armenians extends beyond the Bronze Age, or Armenians were formed by mixture in the
Bronze Age remains to be seen. The question of Armenian linguistic origins is of course separate as it is commonly understood that the Armenian language is unrelated to Anatolian languages and may have arrived in Armenia from the Balkans at around the Bronze Age-Iron Age transition."
"The story of the
Y-chromosomes seems very interesting, although these are not resolved to fine detail. The most interesting aspect of this part of the work is the appearance of haplogroup J in Iron Age samples from Russia, Armenia, and the Altai. This may tie in to the question of the Tocharian origins, which I have claimed were associated with R1b, rather than R1a (as the Indo-Iranians were). The modern Uygurs (who are partially of Tocharian origin) have both J2 and R1b, so were the recipients of West Eurasian elements other than the R1a that so seem to have dominated the eastern steppe, including the Afanasievo.
I continue to think there's no evidence that the Afanasievo is Proto-Tocharian, as it's in the wrong place and 3,000 years before the attestation of Tocharian. "
So, there is no necessary conflict between the findings of Haak et al and Allentoft et al. Allentoft just didn't have the EHG genomes (and had different Yamnaya samples...there was some variation from site to site, afterall), nor did they have the latest statistical tool.