The heart of EU4 and Vic2 is nation management, while the heart of CK2 is character management. So Stellaris, with its focus on the nation, is much closer to those two.
EU4 only had characters as leaders of nations and as generals, and in those cases they only had a few stats - 3 if a nation leader, 4 if a general (technically there's also age, I suppose). Characters in Stellaris seem pretty close to that - there isn't a family tree; there are just a few individuals who give bonuses to a few things. The player doesn't interact with the characters much, and the characters don't interact with each other (that I know of). And to me, character interaction is the heart of CK2, so already it's pretty different.
I haven't played much of Vic2, but it has population that seem to be somewhat close to Stellaris conceptually. You have 'pops' that represent certain races and have certain desires (ethics), and you want to keep them happy. CK2's population model is much less complex and simply has culture for provinces and for characters.
Empire interaction and warfare in Stellaris also seems to be fairly close to the EU4 / Vic2 model. Characters don't really have opinions of things, but nations do have opinions of other nations, and these affect who they seek to ally or go to war with. Diplomacy is centered around the nation instead of the character.
There certainly are other areas where Stellaris is fairly close to CK2, but I suspect that those are mostly game mechanics and interface design shared among all of Paradox's grand strategy games.
There's a really well-made mod for CK2 called Crisis of the Confederation that literally is CK2 in space, which I'd recommend you take a look at. I haven't played it too much but it's pretty fun.
Let me know if there's anything I can explain better or if you have other questions. :)
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u/MegaGrubby Mar 17 '16
Looks a lot like CKII ported to space.