They had 10 fewer cases of heart disease and three more strokes per 1,000 people compared with the meat-eaters.
The research, published in the British Medical Journal, looked at 48,000 people for up to 18 years.
However, it cannot prove whether the effect is down to their diet or some other aspect of their lifestyle.
It said that whatever people's dietary choice, eating a wide range of foods was best for their health.
Half of participants, recruited between 1993 and 2001, were meat-eaters, just over 16,000 vegetarian or vegan, with 7,500 who described themselves as pescatarian.
They were asked about their diets, when they joined the study and again in 2010. Medical history, smoking and physical activity were taken into account,
Altogether, there were 2,820 cases of coronary heart disease and 1,072 cases of stroke.
The pescatarians were found to have a 13% lower risk of CHD than the meat-eaters, while the vegetarians and vegans had a 22% lower risk.
But those on plant-based diets had a 20% higher risk of stroke. The researchers suggested this could be linked to low vitamin B12 levels but said more studies were needed to investigate the connection.
It is also possible that the association may have nothing to do with people's diets and may just reflect other differences in the lives of people who do not eat meat.