The Different Story is a spinoff manga of the Madoka Magica series. But it's more than that. It's not only a spinoff, but also a prequel AND a what-if scenario.
It focuses mostly on Mami and Kyouko, detailing how they first met, then going into a "What if Mami had survived past episode 3" story.
Now I REALLY disliked the anime, so I didn't think I would enjoy this very much. I was proven wrong, very wrong. This manga redeemed pretty much everything I found disappointing about the anime.
It shows, instead of just tells. Kyouko's bizarre little puppet show doesn't really make me feel for her backstory, especially since she again, tells it. In Different Story on the other hand, we see exactly how her story went down, we understand exactly what her father was thinking, and how his behavior affects his family.
Character development in general is beautifully done in this manga, allowing me to better get in the heads of these characters, whereas with the anime I was baffled by the characters and their irrational behavior.
Even the least likable characters are given justice in this manga, and since all of the "shocking reveals" such as what Soul Gems really are and where Grief Seeds come from, are already known to the reader because of the anime, this story is able to better focus its energy on fleshing out the cast and telling a story. It doesn't have to spend four or more chapters trying to mask its true nature in order to shock the audience.
So to anyone who likes the show, or hates it, I recommend giving The Different Story a chance.