Please compare a vegetarian (including eggs and dairy) diet and one
including meat on their health merits only. Assume that both diets
would be reasonably healthy--low in excess calories, sugar, fat etc.
Please use reputable health/medical studies. Please include
consideration of long term health concerns such as cancer and heart
disease.

This is a well written site on the issue.  It cites several major
studies and gives some of their findings.
http://www.mercola.com/article/diet/bible_diet.htm

It is in fact a Christian site (I think) but the content is very
focussed on vegetarian vs meat diet and seems to be fair and
unbiassed.

I didn't read the whole site, but it seems to suggest the vegetarian
diet is significantly healthier than the average meat eater's diet. 
And I'd definately agree with that.  It also suggests (if you read the
right paragraphs closely) that a healthy meat eater would consume much
less meat (6 ounces a day seems to be the standard accroding to the
experts I've read from) would be an even healthier diet.  **note that
most steak houses sell 9-16 ounce steaks as the norm for only 1 meal,
so that throws 6 ounces out the window real quick

This source essentially concludes that it doesn't matter as long as
you are careful to consume everything you need, whether it is from
meat sources or not:
http://www.quackwatch.org/03HealthPromotion/vegetarian.html

Despite concluding that vegetarianism is "unnecessary," they give
information about what vegetarians might be missing in their diets and
what they can do to to ensure proper nutrition.  Benefits compared to
imnivores are also listed.