So if you haven't seen the films or read the books, maybe you don't want to read this. But if you don't mind spoilers, feel free to read on.
As for the film versions, I enjoyed the high futurism of Divergent. But the production design of The Hunger Games is, in my mind, more memorable.
I found Divergent's concept of forced segregation via a coming of age ceremony similar to THGs lottery (but maybe the lottery being more similar to Battle Royale's lotter). I found both Katniss and Tris to be similar strong women characters. I found both societies treated very similarly in terms of the decay of human morality and these women being thrust into unwilling savior roles which they only later reluctantly accept.
I found both societies to be obstinately obsessed with "their ways" in a way where ultra-conservativism and theocracy blend to form a perfect matrimony of unrivaled oligarchies that only want to exert power and control through domination and that is the end goal to obtain before always collapsing back into the same chaos as before due to absolute power corrupting absolutely.
Divergent left off with a happier ending -- more upbeat -- optimistic where Tris is bringing the people together to fight a bigger threat of the outside world. Interestingly, the movie (I don't know about the books) ends in medias res. As if there's going to be more story involving these characters beyond just this moment in their lives.
The Hunger Games covers a bit longer period in Katniss's life and journey from survivor to hero. THG's ending is different from Divergent's in that she leaves it up to the cities to figure things out in the aftermath of her toppling the regimes, whereas Tris seems to be one to continue leading her people.
The Divergent films are always moving. The characters are going here to there and back again. There's always a sense of something is happening. THGs only felt really alive when it was focused on the games themselves. The outside world conflict was rather mundane, and banal, and there was a lot of sitting around and talking and complaining and Katniss never seemed to have her shit together like Tris.
That said, Katniss is the more likable heroine because she is vulnerable and doesn't become a comic-book version of herself. She stays more realistic, and in-tune to the world around her, vs. Tris who becomes this larger than life avenging angel so to speak.
Both film series were enjoyable. Tris found her love right away with Four and Katniss never knew if she liked Peter or Gale more. This gave the films a different appeal in terms of the underlying romances unfolding.
Last, but not least, I have to say that the hand to hand fight scenes in Divergent are some of the best I've seen outside of Kung-fu cinema. Batman needs to take lessons from Four. Seriously amazing choreography here.