The main difference between the two is how much would be paid. For example, the Post 9/11 GI Bill will be responsible for paying the degree-producing courses. The MGIB will also pay for the degree-producing courses, but aside from that, it would also pay for various things such as certification courses, technical courses, licensing, and so much more.
The time that it will take for an amount to be paid will also be different between the two. For the MGIB, you can expect that it will be paid in about ten years. It will be different for the Post 9/11 GI Bill that would take 15 years. The monthly benefits that people can get will also differ.