I've played CIV4 and OW a lot. In both games I win easily on Immortal (Magnificent) and I can win on Deity (Great) sometimes on easy maps.
I never understood what people mean by "spiritual successor" here because I find these games to be very different:
- One uses stacks, other uses 1UPT.
- There are many more units in CIV4 games compared to CIV5 and CIV6. There is orders system in OW, so even if you build big army there is no guarantee you can use it.
- CIV4 economic system is relatively simple - there are only food, hammers and commerce plot yields. In OW there are gold, food, iron, wood, stone, orders, civics, science, training and culture - 10 different plot yields. OW is much closer to CIV5 and CIV6 in that regard
- OW is about antiquity, CIV games are about the whole history timeline. OW relies on events and characters - no such things in CIV games.
I think, from mechanical perspective OW closer to CIV5 and CIV6 than CIV4. The only link between these games in my opinion is Soren Johnson - the lead game designer. I think, the real connection here is that he knows how to make 4X games. Or maybe we have the same taste, idk. Because both games are very strategic, complex and interesting.
So if you like CIV4 I'd recommend you to give OW a try.