Sudden changes in diet tend to result in less success (long-term) for most people transitioning. (http://www.sciencedirect.com/science/article/pii/S0195666312000906
Although I found it mildly difficult at first, I abruptly stopped animal intake upon realizing the health risks. But I found it more difficult to abruptly exclude grains, cacao and wine around the same time I excluded animal products. Later, it became easier to gradually exclude the other high protein foods. I didn't experience the full digestive benefit of a plant-based diet until I eliminated the other high fat/high protein/acidifying diet compromises, too.