It would be a big positive if the world went vegan. Especially at our current population levels.
Food related emissions would drop by 70%.
We would reverse the health issues plaguing the world caused by the meteoric rise in meat and animal product consumption; similar to what's been happening with the decrease in smoking.
Below is an interesting graphic which details the use of land: basically, a very small amount of the world's calories is acquired from animal products, but nearly 80% of the world's food-based farm land is dedicated to it; that means the remaining little bit of farmland used to grow plants for human consumption provides by far the majority of our nutrients. Basically, we would only need to convert 7-9% of our land to plant based food, and we would be able to regain the 68-70% of the world's food producing farmland to be returned to natural habitats. We could reverse the drastic drop in wildlife (the amount of wildlife left in the world is less than 40% of what it was in the 1970s, less than 20% of what it was before the turn of the 20th century).
It makes logical sense from multiple different angles: environmental, ethical, and ecological. The most pressing is obviously the environmental disaster currently in progress. It is occurring slowly relative to our experience, but terrifyingly quickly on a geological scale (currently, about 1 cm every 2 years, which is up from about 1 cm every 9 years in 1900, and 1 cm every 6 years in 1989); the rising economic cost will, unfortunately, only be something that can't be ignored after tremendous and irreversible damage has already been done. If the world went vegan, we would be able to offset this catastrophe by a significant amount. Population growth is a major issue, but we can mitigate the impact (and even reverse some of the current impact) substantially with a global conversion to veganism.
Here's the graphic I promised: