The answer is they can be, but aren't always.
In general, vegetarian diets are lower in saturated fats, cholesterol and animal protein, and higher in fiber and folate than non-vegetarian diets. Consequently, vegetarians tend to have substantially reduced risks for obesity, heart disease, high blood pressure, diabetes mellitus, osteoporosis, and some forms of cancer - particularly lung cancer and colon cancer. In western countries, vegetarians often live longer, on average, than non-vegetarians.
However, differences in lifestyle – not just eating habits – also play a huge role in vegetarian health. People who choose to follow a vegetarian diet are often non-smokers, have a lower body weight, and exercise regularly.
And, of course, not all vegetarians eat healthily. If a vegetarian replaces meat with high-fat cheeses, junk food and so on, they’re unlikely to reap many health benefits – after all, there’s no meat in ice cream, potato chips, or fudge brownies! It’s certainly possible to be a vegetarian and still consume large quantities of high-fat, high-sugar empty calories.
Replacing meat with poor substitutes can lead to nutrient deficiencies in protein, iron, calcium, zinc and vitamin B12. Athletes, children and pregnant females are particularly at risk as their nutrient needs are especially high. Vegans (who eat no animal products of any type) especially need to supplement their vitamin B12 intake. Poor meal-planning, illness, stress and the excessive use of supplements can also cause problems. It's therefore wise to seek professional advice on your dietary needs before making the switch to vegetarianism.
Vegetarian or not, a healthy diet should be low in cholesterol and saturated fat and based around fruits, vegetables, whole grains, and lean protein. Eliminating meat does not automatically make for a healthy diet.