A little bit late for the poll, but I largely agree with Theov. When I'm playing, I'm largely looking at the big picture, strategic level. Being able to identify, oh, there are some Knights invading my lands, maybe they're about to attack me, is useful. Being able to see that Riders are invading is also useful, my response is likely to be somewhat different if they can reach the next city back but the Knights couldn't. The more each civ has unique graphics, without a different effect in game play, the more that ability to see things at a glance is diminished (including when the AI is playing and I'm looking at their moves for brief periods of time until the next unit moves).
Civ IV BTS has variations of skin color based on culture grouping, but the animations are the same. So it's still easy to see a Crossbowman is a Crossbowman, but the Chinese unique unit, the Chu-Ko-Nu, has a different appearance and a different set of attributes and thus a different counter-strategy.
So in general, I'd lean towards, "if the stats are different in at least one way, why not, but otherwise, I'd prefer to have one unit" given the limitations of the Civ III engine. So some civs not having a Medieval Infantry but a different, more culturally-appropriate unit that behaves slightly differently? Sign me up! A "Babylonian Medieval Infantry", "French Medieval Infantry", "Korean Medieval Infantry" with all the same stats but perhaps different appearances? It doesn't add much for me, particularly in the epic game. Maybe a little bit in a period setting, but even then, I'm likely looking at the big picture (I'm not someone who tends to buy Paradox unit pack DLCs just for the visual variety).
Tl;dr: If the flavour shows up in gameplay mechanics, great! If it's only visual, meh.