Differentiating "meat vs. plant" is too narrow of a scope - or too vague of contexts for comparison.
From my understanding in regards to meat consumption and demographics who eat plant-based, these two fundamentals issues exist:
1) Burnt red meat produces carcinogens, and
2) it's the other food that the majority of people eat as part of meat [e.g. a burger with a bun + sugar-loaded ketchup etc], as part of the industrial complex-driven Western diet that are, where people who eat plant-based are likely more conscientious about the food they are overall vs. the general population who eat meat, where also I believe the majority who eat highly processed meat rather than straight animal product.
There are easily enough people and a growing body of carnivore diet followers that could facilitate including them as a comparison, but in reality there should be other groupings like ; and what about including measuring if the participants have historically done water-only fasting (and number of days on average), and number of water fasts they've done during the study period, etc - so then we can see if there's a chance in the distribution?
Such "complex" studies ideally need to have say 100,000 to 1,000,000 participants to get enough diversity - and we'd also want to be careful that the studies aren't co-opted or influenced-captured by industrial complexes and their own interests.
It'd also be ideal to include as part of the participant cohort dietary changes for willing participants, say switching 1,000 to 10,000 people to high-quality high-fat red meat - who perhaps have other arguably healthy diet-behaviour changes to how that cohorts distribution changes vs. the general population.
The issue with such a study is you'd need to subsidize some participants is industrial complexes have maximized accessibility to low quality-harmful "foods" - maximizing profits too to maintain market dominance by also having more profits/money to advertise to remind people to buy their brand - and so high-quality red meat, for example, is too expensive for most people to switch to - even if the long-term cost of cancer treatment and loss of productivity far outweighs the higher initial cost; and so industry isn't going to pay for such a study, it would likely have to be heavily funded through philanthropy.
But to me that feels like a distraction, because have you seen what vegans eat? vegan pizza with "fake cheese", vegan burgers, highly processed hummus on a daily basis, etc.
From my own observations, almost all vegans I know are vegan for ethical reasons, not for health reasons. The fact that it appears to be healthier is just a nice bonus. Therefore, claims that plant-based diets are just healthier because they don't ever burn their burger or put sauce on their bun, feels incorrect to me.