Three 4X game "series", three different approaches.

Sid Meier's Civilization vs Total War vs all the Paradox Interactive games that use the Clausewitz Engine (Hearts of Iron, Europa Universalis, Crusader Kings).
Which one of the series offers the largest amount of realism, especially regarding war and statecraft?

While I am making it a poll, I will also add my own cents.

The Total War games obviously win regarding combat. You got epic battles, no contest. But does that make the comparison fair?
I think not, so... Let's just disregard the battles of the Total War series (despite it being the most important part of it), and just focus on what goes on on the campaign map.
So, regarding what goes on the campaign map... which one of the three offers the highest amount of realism?

WAR

Paradox Interactive games / Clausewitz Engine games

In Paradox games, such as Europa Universalis IV and Crusader Kings II, you can not just attack anyone without declaring war, which is somewhat unrealistic. In Crusader Kings II, you only gain what you define as your casus belli, you need to fabricate claims (which is a huge pain in the butt) to fight your co-religionists, and things like that. It's impossible to re-enact Robert Guiscard, who did not give two ****s about rights and casus belli - he just conquered. Crusades are another weakness - you can only start a war against one sovereign power at a time, so if the Holy Land is fragmented, tough luck launching a crusade against any of the lords who hold a chunk of it (real-life Crusaders didn't really care which Muslim Lord held what land - they only cared that those lands will become Christian).
Other than that though, Crusader Kings II is extremely realistic, with all those characters and dynasty interactions.. It's just sad that the war is a little bit unrealistic. But I guess that's the price you have to pay for game balance... After all, you wouldn't want OP blobs to make an appearance overnight, would you?
In Europa Universalis IV, it gets more realistic: you make your demands at the end of the war, the casus belli being of minimal relevance. You can easily annex your neighbours, but it's not advised, given how coalitions can easily pop up. Overall, Europa Universalis IV is the most realistic you can get... except for battles, off course. And even then, some concessions have to be made, such as peasant rebels not having their own unit type, or the extremely simplified armies (infantry-cavalry-artillery, that's it, not other variation).
Another thing that EU4 gets right while CK2 gets wrong is passing: in EU4, you cannot lead your army into foreign provinces without either declaring war or asking for access, while in CK2, you can, which is unrealistc. I doubt that any real-life Christian Kingdom would have allowed Jihadists to march through their lands, or vice versa.

Obviously, it's a limitation caused by the usage of Risk-style maps, but do armies automatically know which city are they besieging?

Total War games

In sharp contrast, in the Total War games - the most recent TW game I have played is Medieval II Total War, so excuse me for ignoring all the new additions that later games bring to the table - diplomacy is somewhat simplified. You can start wars at will, which is pretty realistic. I don't know if it's realistic or unrealistic that territories you conquer immediately become yours, without any formal peace treaty being necessary to legitimize your rule over them, although the M2TW does pay this fact a bit of lip service in the form of your enemies demanding you to hand them back their provinces when asking for peace.
In the original Medieval Total War, marching your army to another empire's province meant war, which is half-realistic (I know, limitation of the Risk-style map, but still... I doubt your allies would immediately declare war upon the presence of your army), while in Medieval II Total War, you can just march where ever you please, which is totally unrealistic, although... Maybe it could be made realistic if non-allied armies marching through your lands created devastation, forcing players and AI alike to react violently to foreign non-allied armies marching through your lands (which would mean WAR, if the army belonged to a neutral faction).
But then again, concessions have to be made for the sake of game balance. Besides, if you played Total War with 200+ factions instead of 32~, your computer would burn - or the game would simply lag terrible. Even with Stainless Steel, my laptop takes almost forever to process the turns.

Oh, and did I mention that you have to manually find the enemy city to besiege it? Pretty realistic, if you ask me. After all, real-life armies had to do recon jobs too, and you can't be entirely sure where is the enemy city.

Civilization games

Warfare might be the weakest point of the Civilization games. It's simplified to be as simple as simple as possible, and although it has become more and more streamlined as installations went, it never really got me. Though, I might add, it pretty realistically simulates shield walls: whoever has more weight will make the frontline move in the direction it wants to move in.
However, you can pretty much only attack one unit at a time - the top unit of a stack. Which is obviously unrealistic, but I guess it's simply one of those acceptable breaks from reality that we have to accept, for the sake of game balance and yada yada ya...
However, one thing that IS realistic about the way wars are done in the Civ games is that you have to discover the enemy city first, just like in the Total War games. The lake of a Risk-style map means that you can't just say "conquer this province" and be done with it. No. You have to send scouts to discover the position of the city, then drive all your troops onto it, leading them into a clear suicide attack that is akin to the Assault option in sieges in both CK2 and EU4.

Money, dear boy, money...


Paradox Interactive games / Clausewitz Engine games

In CK2, economics are rather simplified. You have your gold, piety and prestige. You don't really have trade resources. Not very noteworthy, not very realistic.
In EU4, we get trade resources, and they are handled somewhat realistically. You get monopolies, you get development, you get control of trade notes, all awesome.
Also, in both CK2 and EU4, we have corruption and loans, which add to realism. None of the other two have that.

Total War games

Economics and trade might be the weakest point of the Total War games, and arguably the building system is as unrealistic as in all the other games. Sending merchants to acquire foreign goods generates money for you instead of taking away your money like it would in real life. However, in earlier games, such as Medieval Total War, at least some lip-service was paid to reality and some resource-dependent buildings were introduced.

Civilization games

Economics are arguably the strongest point of the Civ games, and trade is arguably the most realistic. Don't have a certain good? Don't have the necessary military might to acquire it by force? Then trade! This way, you can actually build all the juicy stuff that gives you advantages from having access to certain resources.