Ocha-ken: Chokotto Monogatari

They both have a different art work style than normal 

Both have narrators commenting on the animal's lives, calming background music and atmosphere in both. 

Simple stories about dogs that are food (in Jagainu-kun other animals are food too) . They are very relaxing series with light animation and only a few minutes long per episode. Certainly quaint series to see on a lazy Sunday morning. 

they are both short anime under four minutes per episode, and both give lessons during/after each episode.  

Both are extremely short(around 5 minutes?), and very cute. Damekko Doubetsu will have more laughter, but Ocha-ken has a sweet and 'awww' inspiring aspect about it. Both series are about animals; Damekko Doubetsu about useless ones, Ocha-ken about tea dogs (and cats).