Pfizer/BioNTech vaccine seems safe - I don't know where you heard otherwise.
Pfizer/BionNTech vaccine is also likely more effective than Sputnik V (that on the other hand seem more effective than AstraZeneca).
The J&J (or Janssen) vaccine might also be a game-changer for developing countries, as it is similar to both AstraZeneca and Sputnik V, but it has also been tested with only one dose.
However, I see nothing indicating that the EU delayed this due to cold war bs. You simply don't start processing an application until you receive it, and Sputnik V application was as far as I see only sent in after they had results from phase 3 tests, which is completely normal - you don't authorize without a test.
On the other hand the name "Sputnik V" and Russia skipping precautions and stating that they began using it before phase 3 reeks more of cold war bs from another player (and I still find it odd that Putin announced that one of his daughters got it - but not which one). It's good that it still seems to work, but even the Lancet study has some odd parts - in particular two covid-deaths among the vaccinated (I have previously given one likely explanation, and I don't see the vaccine itself as the problem - it's just that it doesn't look good).
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Found an interesting comparison of the success of different states in the US in combatting covid-19:
https://www.economist.com/united-sta...19-differently
Basically the largest two states differ a lot: one democratic (California) trying to lock down things, and another republican (Texas) trying to keep it as open as possible.
Obviously California has a lower death toll per capita, the interesting part is that the difference isn't that large: 104 vs 127 deaths per 100,000 (the numbers are of course increasing, and it's still about 8,000 extra deaths); indicating that it isn't easy to completely stop the disease.