According to the BBC up to 16 June there were 389 reported cases of blood clots with low platelet levels in people who had the AstraZeneca vaccine in the UK, with 68 deaths. In the same period there were 12 cases in people given the Pfizer/BioNTech vaccine, with one death, and none in those receiving the Moderna vaccine. By this date about 16.8m Pfizer/BioNTech, 24.5m AstraZeneca and 0.73m Moderna vaccine first doses had been administered in the UK.
My older children have decided to wait for the Pfizer on the basis that Covid poses little risk to them, so there is no rush to take a poor cousin vaccine. Each to their own.