My understanding was, that the delay was mostly because the EU went through a fast track version of the normal certification process while the UK and the US used emergency certifications.

IMHO, it is not important who started first, but about how fast you get to 65+% of vaccinations. I don't have any issue with delays early on, but right now this mixture of political power games, blaming, panic and agenda pushing is risking the whole European vaccination campaign.