Screenshot of Biden's claim of 1/160,000 hospitalization rate among fully vaccinated: https://pbs.twimg.com/media/E-4NQBFWEAMzATQ?format=png&name=...
Current rate of known non-fatal hospitalization from COVID-19 among the fully vaccinated is 5.1/100,000 which is 8 times the rate Biden mentioned. It is also 3 times what it was on 6/1.
Current rate of known deaths from COVID-19 among the fully vaccinated is 1.2/100,000. Biden did not make a claim about that number. However, the fatality rate is 4 times what it was on 6/1.
Therefore, known hospitalizations and deaths from COVID-19 among the fully vaccinated is rising faster than the current number of fully vaccinated individuals.
However, this is hard to interpret because there is a lag between arriving at "fully vaccinated" status and getting infected. Then, there is another lag before one might be hospitalized. Then, there is another lag before one might die.
From the way the rates have been rising, it seems to me we have not arrived at a point where we can deduce a decent guesstimate of real life probability of hospitalization and death among fully vaccinated. It seems we'll be lucky to have the hospitalization rate stabilize around 1/10,000 and death rate stabilize around 3/100,000.
Note the phase3 trials lasted about 5-6 months[1,2] and they did not enroll a lot of people at risk. Now, it seems like, there is consensus that whatever protection the vaccines confer doesn't last more than five or so months past achievement of "fully vaccinated" status.
As for being able to compare with "unvaccinated", we need proper data for that, but there is not much out there.
Statements like "98% of hospitalizations since January 1 were among the unvaccinated" do not mean anything as the composition of the population is not constant lumping everything together removes information needed to properly evaluate what's happening.
[1]: https://www.pfizer.com/news/press-release/press-release-deta...
[2]: https://www.npr.org/sections/health-shots/2021/02/19/9691430...