Having gone through both programs, I can say without a doubt that they were both amazing and worth the time (and equity in Imagine K12's case).
As with any accelerator/incubator, you need to match your goals and the stage of your company with the program itself. Deborah describes the differences perfectly. From our experiences:
4.0 Schools was great for us when we were in ideation phase and needed to do a lot of customer development. We had a small amount of product built and even had to step backward to focus on what our customers needed instead of the product itself. It also started out deeper dive into knowledge of education and the ed-tech space.
Imagine K12 was perfect for our stage when we were just starting to get some traction, had the product a bit more flushed out, and needed to take our company to the next step. With it's YC style (and connections) it really lets you learn how to speed up your internal and external growth from the best people possible.
We were able to raise investment off the proof-points we obtained during and immediately after each program. Again, if the stage of your company is appropriate, either program is great.