Is there any evidence that leans towards either 3 or 8 weeks gap as providing better protection than the other to an individual?
Providing a second dose earlier is recommended for the individual so that they will experience "full" protection earlier rather than later. As the WHO has noted, spreading out the second dose "enhances peak antibody generation in older people," which suggests "extend[ing] inter-dose intervals will result in a good immune response, even in older adults." I could not find data on vaccine efficacy for the Pfizer vaccine after extending dose intervals. For the AstraZeneca vaccine, extending the dose interval does increase the vaccine efficacy (from 56% for an interval of 4-8 weeks to 78% for an interval of more than 12 weeks).
The WHO updated their interim recommendations on June 16, 2021. In the updated recommendations, they include a section on deferring the second dose. Here is the relevant part of that section:
WHO acknowledges that a number of countries face exceptional
circumstances of vaccine supply constraints combined with a
highdisease burden. Some countries have therefore considered delaying
the administration of the second dose to allow for a higher initial
coverage with one dose. This is based on the observation that efficacy
has been shown to start from day 12 after the first dose and reached
about 89% between days 14 and 21, at the time when the second dose was
given. No data on longer term efficacy for a single dose of BNT162b2
currently exist from Phase 3 trials, as the trial participants
received 2 doses with an interval between doses in the trial ranging
from 19 to 42 days. Neutralizing antibody responses were shown to be
modest after the first dose and increase substantially after the
second dose, and the second dose increased the efficacy against
symptomatic disease to 95%. Post second dose studies showed that
immunogenicity in terms of neutralizing antibodies is increased with a
longer inter-dose interval to 12 weeks (10) highlighting that extended
inter-dose intervals will result in a good immune response, even in
Some countries have chosen an inter-dose interval of 12 weeks. Based
on post-introduction vaccine effectiveness studies from these
countries, data on persistence of post dose 1 effectiveness are
currently available up to 10 weeks in the context of the ancestral
virus and the variant of concern Alpha (B 1.1.7) (11). Evidence on the
impact of variants of concern other than Alpha (B1.1.7) on first and
second dose vaccine effectiveness is only just emerging.
Effectiveness after a single dose of vaccine against COVID-19
associated with Delta (B 1.617.2) was lower than that against Alpha
(B.1.1.7), whilst two dose effectiveness was similar for these two
variants (12). These data highlight the importance of providing a
second dose of vaccine in the context of circulating variants of
concern that may lower the effectiveness of a single dose.
From reading the full report, the WHO's concern is not that efficacy will be worse when spreading apart the doses (once the second dose has been given), but that people with only one dose are more vulnerable before the time they receive their second dose.
The WHO does conclude that:
In conclusion, for countries that have not yet achieved high vaccine coverage rates in the high-priority groups who are experiencing a high incidence of COVID-19 cases combined with vaccine supply constraints, WHO recommends that such countries should focus on achieving a high first dose coverage in the high priority groups by extending the inter-dose interval up to 12 weeks.
Bonus for those who read all the way here.
The UK has notably also administered the Oxford/AstraZeneca vaccine. For this vaccine, the WHO writes:
Exploratory analyses were conducted of vaccine efficacy 15 days or more after the second dose, according to the interval between the first and second doses. For about 59% of participants the interval was 4–8 weeks, for 22% 9–12 weeks and for 16% more than 12 weeks. The estimates of VE increased significantly in these 3 groups, being 56%, 70% and 78%, respectively.
Vaccine efficacy for the Oxford/AstraZeneca vaccine did increase by expanding the dose interval to 12 weeks. The corollary is that during those 12 weeks between the first and second dose, people are not protected as well.