I've decided to go for the deeper base for the two instances of Lit/CWg/CP that I was planning - a litter carrying the Great Sun for my Mound Builder Americans and a ceremonial chariot for my Javanese. I'll turn both into little vignettes - the litter will have an escort of armoured nobles at the front of the base and the ceremonial chariot will carry only the general and parasol holder, but will be surrounded by infantry and followed by musicians.
I'm drooling at the sight of "Gomat's" Olympias Lit Gen element. Love all the periwinkle blue. Just seems so Greek... Awesome vignette.
Like others here, I have used whichever depth (40 or 80mm) yielded the right "look". For most of mine, Pope on his Golden Throne, Great Sun King, and Pharaoh's Litter (below), I have used the deeper base.
But for my Great Prophet and his Pup Tent, I went with the smaller, square base.