Much to the chagrin of some fans, the second season of the wildly popular One Punch Man was handled not by Madhouse, but by J.C. Staff. While this studio swap has made headlines, it's not the first time that such a thing has happened. In fact, there are plenty of anime that switched studios at some point during the development process. Often, this takes place between seasons, or before a reboot.
Why would a property being managed by one studio move to another? Reasons vary, but they tend to involve logistical issues rather than anything especially dramatic. Anime studios typically don't own the rights to the anime they produce - typically, they work as contractors and must bid to take charge of a desirable property. Sometimes it's because the studio simply doesn't have the time or manpower to take on a sequel series, or because the director had a change of heart. In some cases, as with the Fruits Basket reboot, it's because the author of the manga that the anime was based on was dissatisfied with the first attempt and wanted the new series tackled by a new staff.
In some cases, a studio change can feel like a downgrade - that's definitely true of Psycho Pass, which decreased dramatically in quality when it moved from Production I.G. to Tatsunoko Production. But at other times, like with Fate/stay Night's swap from Studio Deen to ufotable, the changes are for the better. Sometimes, the change hardly seems to make a difference. No matter how the change impacted the series itself, it's still interesting to know about the show's production history.
Originally, Fairy Tail was produced by A-1 Pictures and Satelight. After that, its two sequels were produced by A-1 Pictures and Bridge. The reasons for this change were never confirmed, but there are significant differences between the first series and the two that came after.
These differences are many, but they boil down to a change in tone, character designs, and color pallette, and in adherence to the manga. Satelight's season was brightly colored and light-hearted, while Bridge's seasons are drawn with darker, more muted colors that underscore the more serious themes the seasons deal with. Bridge is also more diligent about closely following the manga instead of relying on filler arcs.
Madhouse is not known for creating sequels - some anime fans even call it the Madhouse Curse. It's not that they never make sequels - Card Captor Sakura Clear Card is a recent example of a sequel they did take on - but it's uncommon. This tendency may have been why they passed Gunslinger Girl onto Artland during its second season. This anime, which deals with a corrupt Italian government organization that takes young girls with serious health problems, gives them cybernetic enhancements, and then forces them to become soldiers, had a pretty good first season. While the second season retained its characterization and plotting, the animation quality went down.
Most anime that change studios only do it once, but Minami-ke, which is a slice-of-life series about the everyday lives of the three Minami sisters and their family, is an exception. The show has four seasons and was produced by three different studios. Daume, a small studio that's best known for Shiki, took charge of the first season, while Asread of Future Diary fame took on the next two. At first, Asread changed up the show's aesthetics, altering the character design, color palette, and even the appearance of the main characters' school, but by Season Three they tried to steer it back toward the series' original designs.
The fourth season, as well as an OVA, were handled by Studio Feel. The reason for all these changes has not been publically addressed.
Log Horizon's first season was handled by Satelight, and the second season was scooped up by Studio Deen. While opionions on the quality of the second season vary, the general consensus seems to be that the quality decreased after the first season. The pacing began to drag where it had previously been sprightly, excess time was spent on irrelevant side characters, and a love triangle from the first series that many found irritiating took up far more space than it had before. For this reason, many Log Horizon fans ditched the series in the second season.