Where to begin!
Faction wise I love the Tokugawa. They start off in a really interesting position; a vassal to the Imagawa which means you can't declare your own wars. Their colour scheme is nice too and it's cool when Ieyasu comes of age. Their starting location is also perfectly suited to my playstyle; I can recruit good light cavalry which is used to great effect beside my early yari ashigaru armies. Later bolstered by Katana samurai from Owari once the Oda are defeated, which is always priority number 1. Can be quite a challenging campaign, sometimes the Imagawa betray you quickly, other times they drag you into wars with other powerful clans like the Takeda or Hojo, forcing you to consider taking an honour hit and betraying them.
My favourite unit is probably Katana Cavalry, versatile and powerful. I do enjoy the Kisho Ninja units but they feel more of an 'easter egg' because they're not really as useful as they were intended to be it seems.
In Fall of the Samurai; none of the factions really stand out as favourite,
maybe the Nagaoka. But my favourite unit are the Parrott Guns. The devastation they can unleash makes their high cost worth it every time, once I have access to them I find I am rarely in trouble during my battles.