K-On!: Ura-On!

Same kind of thing, short funny episodes based around the characters from the parent show. 

Both are short specials which take characters from parent anime and make them into chibi style. Both are mainly for comedy purpose and have almost no story. 

Both are short specials, made as spin-offs of original series. Both have chibi-styled characters and are based mainly on comedic dialogue. Both are comedies and both have short episodes. Difference is that Shingeki no Kyojin Picture Drama comes froum shounen anime while K-On: Ura-On comes from slice of life anime. 

Both are short episodes about bands. 

Comic reliefs for respective series. K-ON doesn't really need comic reliefs though. Purpose of these short bonuses are nothing short than boosting DVD sales, that sound like a similarity an adult may talk about. 

Spin-offs of main series, characters are in chibi forms