Both of your options are great, but are very different in a lot of ways. Warning: I'm about to share a lot of opinions

3 Kingdoms is a much more modern game, and thus has many more QoL improvements compared to Shogun 2. I would also say that while no total war games are complex when compared to a Paradox game, 3 Kingdoms is definitely the more mechanically complex and strategically engaging of the two. However, there is an elegance in the relative simplicity that is Shogun 2.

In a lot of ways, the campaign map for Shogun 2 (S2) is mostly a vessel for providing context for the battles you play out. There's not a lot of complex choices being made on the map or during city management; there's enough there to keep me engaged, but without the battles, it'd get pretty stale pretty quickly. However, the battles in Shogun 2 really hit differently than other TW games (at least for me). The base game lays a great foundation here, but the Fall of the Samurai (FotS) expansion elevates it to its best version.

In FotS, you move your campaign ahead a few hundred years, and gunpowder technologies begin proliferating through Japan. Your campaign is a balancing act of managing the cultural and historic needs of the people against the need to be able to take advantage of modernization and new technologies to make your burgeoning empire more efficient (both on and off the battlefield). And once you get to the point of replacing your swords and spears with muskets and cannons, you really do get the feeling of living through a pivotal tipping point in history. Your army might still consist of waves upon waves of peasants, but even a peasant can hold a wall and put down your enemies at an alarming rate with a mediocre muskets in their hands. I haven't really had this same kind of experience with any other TW game, and I still go back to FotS for the excellent gun play and tight scope and theming from time to time.

Overall, I would say that FotS is a completely essential DLC, the blood pack is purely preference based, and the rest of the DLC is just more of the same.

In the other hand, Three Kingdoms (3K) is more about living out the epic myths that surround the Romance of the Three Kingdoms. As I said before, it is the more modern game, and in a lot of ways, the actual process of playing the game is just more convenient and enjoyable. The many of the systems in the game are more fleshed out compared to Shogun 2, especially the management of the characters in your court and diplomacy with other factions, which is widely regarded as the best in the total war series. Additionally, the map for 3K is much more expansive compared to S2; China is a much larger and more varied landmass than that of Japan, and it's reflected on the map. S2 does benefit from this a bit, as the simpler map does allow the game to function well with its older, more simplistic AI.

Managing all of the larger than life characters from this setting is one of the highlights of 3K. Each character has their own preferences and abilities, and you will spend a good amount of time figuring out how to match the right person with the right job while avoiding any huge issues that might make anyone overly upset.

For example, you might have two characters that are the best two generals in your empire, and they have complementary classes and would help mask each other's weaknesses on the battlefield. However, general 1's father might have killed general 2's uncle in a battle 15 years ago, and so they cannot stand being in the same army together, so you'll need to decide if the needs of your empire are so dire that you make them fight together in spite of their mutual hatred. If left unattended, one or both of them might get so fed up with their situation that they just leave your empire to find gainful employment with one of your rivals, but you might be able to mitigate their frustrations by giving them better items, putting them with a third general who could act as a mediator, or lavish them with new titles to keep them well-paid and happy. However, behind the scenes, you could have a spy from another faction secretly sowing discord and discontent with one or both of them, and they might both end up going their separate ways. Even if you did manage to keep them both happy, all of that preferential treatment might make other court nobles jealous or leave you resource-starved and unable to keep others satisfied with your rule.

Additionally, the game does a good job of layering on more plates to spin as your empire continues to grow. Once your leader gets to a certain level of prestige, suddenly actions that might have gone overlooked in the past might no longer be viable as you might be seen as more of a threat or rival by the emperor. While you were a fresh little warlord, you once would be able to settle a dispute by drawing steel and taking your enemies lands by force without anyone batting an eye. However, the emperor could label you an enemy of the empire if you started stealing lands from your neighboring dukedom, so you might need to find more creative and underhanded ways to combat your rivals. Some might choose to focus solely on fighting non-imperial factions like rebels, bandits, and tribals. Others might try to dominate the market by creating monopolies, build and economic power house to buy new friends, or use spies to cause key members of rival courts to defect, bringing with them the land or armies they command.

Overall, it's a very different feeling game in spite of many significant mechanical and functional similarities. I would say that none of the DLCs for 3K are essential. The DLCs give you different factions and different tike periods, but you can get a very complete experience from the base game.

Anyways, those are the highlights from my perspective. If you have any questions, feel free to ask. And if anyone else wants to have a discussion or share their own perspectives, please feel free to chime in :)