I rode the Divide a couple summer back and thought each section presented a unique challenge, but from my perspective, southern Colorado and New Mexico was the hardest. Maybe it was because I was nearing the end of the tour and wearing down, but the climbs seemed steeper and rockier in southern Colorado and northern New Mexico, and the New Mexico desert may have been the most remote section on the route. The heat and lack of water available over a few stretches also make that a hard section. Going into it fresh might make a difference.
If I had to pick an easiest section, I might give that to the middle section (Wyoming/northern Colorado). You need to be prepared with water for the Great Basin, but the road surfaces were overall pretty good, and the major climbs were spaced out nicely that you could get a good break in between them.
I think should throw a fourth segment in there and do the Canada/Montana portion twice