Here is my rough rundown.
There is a 'Battle Story' in the back of the Japanese Zoids boxes. Each Zoid had a fragment of the 'Battle story' dealing with that zoid models involvement in the war.
Generally, it was about a long war between the Helic Republic and the Zenebas Empire. Other factions included the Guylos Empire and the Neo Zenebas. No real hero mechs(zoids) here, more of an epic scale intercontinental war.
The animes operate on a different plot from the 'battle story'. Its still about the Empire vs the Republic but we have 'Hero' mechs.
For example, in the Battle-Story, it was the introduction of the Republic Madthunder which stemmed the assault of the Imperial Death Saurer. In the anime, predictably, the Death Saurer gets taken down by loud kid in a hero zoid who gets all his victories by screaming and throttling forward while the hero mech does its slow-mo melee attack-which-defeats-everything.
Generally, the Chaotic Century and Guardian Force animes are good in my opinion. New Century Zero (treat it like a comedy), Fuzors (especially Fuzors) SUCK! Did i TELL YOU fuzors SUCKED? Never watched Genesis, but since the title character is some 12 year old kid in a liger again, well......