Lancet: We also investigated infection rates after the first vaccine dose in a subset of 67 293 app users who received BNT162b2 and 36 329 who received ChAdOx1 nCoV-19 in the study period.

We compared the test results of this population with those of 464 356 unvaccinated app users who had a PCR or lateral flow test (covid test) result between Jan 4, and March 10, 2021.

12–20 days after vaccination, infection risk in the vaccinated group was significantly lower than in the unvaccinated group.

Risk Reduction
Pfizer (BNT162b2): −58%
AstraZeneca (ChAdOx1 nCoV-19) −39%

From 21-44 days AZ went up (down) to -60% and Pfizer -69%.

The glaring problem with this study is that it's not a fair comparison. Whereas vaccine recipients must present symptom free to receive a shot, unvaccinated people are most likely to get a Covid-test only when they do have flu-like symptoms.

It stands to reason that the second group is going to have a much higher positivity rate.

If you compared infection rates of an unvaccinated group with no symptoms with an unvaccinated group with symptoms then you may well get similar results.