I’m not sure you can just make a direct comparison between protein amounts, so that control may not work as you intend. As I understand it, your body metabolises dietary protein into amino acids, which it then uses to synthesise the protein it needs (that’s why even if you eat meat, your body isn’t made up of cow protein it’s made up of human protein). Meat eaters get most of their protein from meat and dairy products which contain complete proteins in the sense that they contain all the amino acids humans need. There aren’t that many complete proteins that are vegan so vegan diets tend to include a mix of grains and pulses. These give all the amino acids your body needs to synthesise protein but have a different balance meaning that 100g of plant-based protein != 100g of meat-based protein, and keeping them exactly the same by weight might actually be unhealthy for the vegan group.

As I understand it, the way to achieve what you’re going for would be to calorie-control both groups and then set a percentage of calories from protein and specify for the vegans what the breakdown needed to be between grains and pulses. That would be a right royal pita to manage so might be more overhead that it’s worth idk. On the other hand it may make the study more definitive.

I’m always skeptical of studies like this because the group that shifts to a vegan diet might just be shifting to a healthier diet in general and therefore that might be the effect you’re seeing rather than an effect that shows veganism is better than meat eating per se. Like what if people in a third group kept eating meat but had some sort of controlled meat-eating diet. They may well see an improvement just because now they’re thinking about their diet to meet the restriction and so are making healthier choices as a side-effect.

Source: not an expert but have been vegetarian for nearly 40 years at this point and vegan for about 10ish of those. Veganism kind of crept up on me so I don’t know the actual day I started. I don’t have an opinion about whether anyone else should eat meat. My choice is just about what I eat.