I use the following system to calculate the final score:
In each of the five categories (Story, Art, Sound, Character(s), Enjoyment), a score can get 2, 4, 8 or 10. 2 for something I find truly bad, 4 for something that just isn't good enough, 8 for fairly good and 10 for outstanding.
The sum of the score is divided by 5 and the score is rounded to the nearest integer (More than or equal to .5 rounds it up, less than .5 rounds it down).
STORY (10):
As with many Gundam series, it's about a young boy who becomes part of a small military force that opposes greater military forces. There are themes concerning authority, youth, war, death, romance and politics, though it seems that the main theme is "WAR IS BAD".
I found it to be well executed, although slow from time to time. The story of AEUG isn't a complicated one, but somewhat captivating. Kamille's growth throughout the series is something worth watching, even if the ending can be a bit of a downer.
ART (10):
Zeta Gundam had some really good mecha designs, especially Gundam MkII and the titular mecha, Zeta Gundam, which ranks as my favourite Gundam of all. This series also introduces the beauty that is the Qubeley, so it's solid on the design front.
Animation is mostly on a pretty average level, but every now and then they surprise you with some really detailed and beautifully animated scenes.
SOUND (10):
Disregarding the terrible, terrible j-pop openings Zeta Gundam had in its country of origin, the soundtrack is fit for an epic tale of space warfare. The voice actors do a great job and some of the speeches and yells during battle make them sound as if they were super robot pilots.
CHARACTERS (8):
An overall good cast, but some of the characters can be really annoying at times, especially Katz. If it hadn't been for him and a certain character doing something I feel was unsupported by the overall story, this might have scored a 10. Be prepared that you may dislike Kamille, the main character, quite a bit. Although I do not, a lot of people are disturbed by his constant whining and disrespect towards others.
ENJOYMENT (10):
As a mecha fan, there's a lot of fanservice with all the different suits and armors used in this series. The tale itself, the operations and some characters from the first series just add even more viewing pleasure. It really is quite a classic.
FINAL SCORE:
48 * 0.2 = 9.6, rounded up to 10.
RECOMMENDATION:
It's 50 episodes long, so you better be prepared for some slower parts here and there. There's a lot of war and death, and the action is often there to say that war is bad, which sets a somewhat grim tone over everything.
However, if you want a war drama set in space, this is a truly good one.
Though if you want to watch this, I recommend watching the series that came before this first, Mobile Suit Gundam, or the Mobile Suit Gundam movie trilogy which summarizes the first series. This will help with background for both the setting and several characters.