Yes, and yes. There are a number of studies of vegetarian/vegan populations indicating that in general, their health is better, and life expectancy greater, than their omnivorous counterparts. Bear in mind, however, a number of provisos: 1) since modern medicine is very good at keeping alive, but not at preserving true vitality, eating well is much more likely to add life to years, than years to life; 2) many parts of the globe in which vegetarianism is widely practiced (e.g., India) are subject to other, potent, countervailing health influences (e.g., crowding, poverty, etc) that conspire against longevity; 3) there are no randomized trials comparing very different diets and examining effects on life expectancy for obvious reasons- such trials would require people willing to be randomly assigned to a vegetarian vs. 'carnivorous' diet for decades, and the trial would require a large sample and many, many years to conduct. Thus, the best evidence-based answer to your question is derived from non-randomized trials. That is fine, but it carries baggage. It may be, for instance, that a population of vegetarians differs systematically in other ways from a population of omnivores with implications for health outcomes. Finally, your question refers to 'carnivores,' but you presumably meant that somewhat figuratively. There are no truly 'carnivorous' human populations- they would die out of scurvy, for one thing. But there are populations, such as the Inuit, that eat a very predominantly animal-food-based-diet.

There is extensively referenced coverage of these topics in chapters of my textbook, 'Nutrition in Clinical Practice, 2nd edition,' 2008. Here are a few relevant citations:

1: Fraser GE. Vegetarian diets: what do we know of their effects on common
chronic diseases? Am J Clin Nutr. 2009 May;89(5):1607S-1612S. Epub 2009 Mar 25.
Review. Erratum in: Am J Clin Nutr. 2009 Jul;90(1):248. PubMed PMID: 19321569;
PubMed Central PMCID: PMC2677008.


2: Leitzmann C. Vegetarian diets: what are the advantages? Forum Nutr.
2005;(57):147-56. Review. PubMed PMID: 15702597.


3: Vegetarianism: addition by subtraction. An increasing number of studies are
finding health benefits from a low- or no-meat diet. Harv Health Lett. 2004
Feb;29(4):6. PubMed PMID: 14980877.


4: Willett W. Lessons from dietary studies in Adventists and questions for the
future. Am J Clin Nutr. 2003 Sep;78(3 Suppl):539S-543S. Review. PubMed PMID:
12936947.


5: Singh PN, Sabaté J, Fraser GE. Does low meat consumption increase life
expectancy in humans? Am J Clin Nutr. 2003 Sep;78(3 Suppl):526S-532S. Review.
PubMed PMID: 12936945.


6: Fønnebø V. Mortality in Norwegian Seventh-Day Adventists 1962-1986. J Clin
Epidemiol. 1992 Feb;45(2):157-67. PubMed PMID: 1573432.


Best,
DK