I don't think that there is a huge difference in digestion times but in general vegetables are more easily digested than meats. Meat contains a lot of protein and fats. These contain amide and ester chemical bonds which are time consuming to hydrolyze with stomach acid. Vegetables on the other had have a large water content and also carbohydrates and fiber. Carbohydrates are polysaccharides that are broken down into simple sugars for absorption. Fiber is composed of large, insoluble saccharide polymers that are not well digested by the body and simply pass through the digestive system and excreted as waste.
Vegetables because they are usually made out of mostly water therefore the only part of the digestive system working is the large intestine which absorbs the water from the vegetables.