Zeta Gundam takes place in UC 0087, 7 years after the end of One year war in MSG (0079). For many Gundam fan, including myself, Zeta is the best Gundam series ever with great characters, plot and mecha design. It tells the story of Camille Vidan, a 16 year old newtype fighting in the war between AEUG (Anit-Earth Unified Government), Titans (Branch of Earth Federation) and Zeon.
Gundam ZZ takes place in UC 0088, following the story of Zeta Gundam with a new set of characters and mechas. However, it has a much lighter tone than the epic setting of Zeta. Some of the characters and events can be considered as childish in the first half of the series. After about 20 eps., the story starts to pick up the "normal" Gundam feel. It is still worth seeing for any Gundam fan, especially UC fan.