Forget the CDC study, I agree with the above poster and will detail why later.
THIS is the best study so far..It's huge (800k participants) and does not bias the results using only pre-hospitalised Px

[link to www.medrxiv.org (secure)]
Comparing SARS-CoV-2 natural immunity to vaccine-induced immunity: reinfections versus breakthrough infections

Results
SARS-CoV-2-naïve vaccinees had a 13.06-fold (95% CI, 8.08 to 21.11) increased risk for breakthrough infection with the Delta variant compared to those previously infected

After adjusting for comorbidities, we found a 27.02-fold risk (95% CI, 12.7 to 57.5) for symptomatic breakthrough infection as opposed to symptomatic reinfection,

Nine cases of COVID-19-related hospitalizations were recorded, 8 of which were in the vaccinated group and 1 in the previously infected group (Table S1). No COVID-19-related deaths were recorded in our cohorts.

ps CDC: (bear in mind they make a lot of money from vaccine patents, a VI they should declare with every study they sponsor, and NEVER do..)