Throwing in 2 cents from a newbie perspective: For me (first game of RoM/AND currently in progress), the warlord chiefs are certainly a very noticeable addition. When they became available, they were by far the most powerful unit I could build. It felt almost compulsory to build one, since the AI built them too, and I didn't have a good counter at that time in case one of the warlords attacked me. Using my own warlord was confusing at first, it took some time getting used to the fact that I can enter (but not attack) friendly cities.
My current strategy is to station the warlord chief in a city which borders on three neighbors (all of which I have Open Borders with) and prey on passing units. I gave my warlord the "Morale" promotion so that he can often go on hit-and-run missions, ending the turn in the safety of the city. It's interesting because of the novelty and the ability to secretly badger my neighbors so early on, but I have two concerns.
One is whether the AI is actually able to use the unit n a decent way. The other is whether the warlord chief might be so powerful that every early military strategy necessarily has to revolve around him, this might feel forced after a while. But I haven't played enough AND to build an opinion on either of these concerns, they are just thoughts that cross my mind while playing.