I have seen all the Hunger Games movies (twice) but I never read the books. Conversely, I actually read Divergent, but only saw the first movie in the series before dropping it completely. ^^; So that's where I'm coming from.
I think, based on everything I've heard and seen of both franchises, HG is the better series by far. But personally I just think it also has a much smoother concept. The action part is the Hunger Games, and the drama part is also the Hunger Games. Katniss and Peeta's relationship only takes the turn it does because of how they are pressured to use it to their advantage during the Games...which is honestly more than I expected before I actually got into the series. ._. That's pretty smart writing.
Divergent, on the other hand...the drama part is Tris trying to fit into the Dauntless faction, and the action part is...apparently some evil scientist world-domination BS extra plot that honestly felt very tacked on even while I was reading it. =/
Divergent's concept feels like something whose stakes should be almost exclusively political and ideological...who set up this system and why? How can we take it apart? What will the consequences be, how will those in power push back...?
But apparently that's not 'exciting' enough, so they just threw the protags into some random war before they even had time to think about these things, let alone try to act on them.
And I think that's a large part of the reason they changed Tris' character 'design' so drastically for the film: basically, the author practically set themselves up to have Katniss 2.0, despite writing a tiny, frail girl as the protagonist.
Tiny and frail could work in a story about fighting metaphorically for change as a community of people who don't fit into the molds society set out for them. It doesn't work in a story about becoming a literal soldier...at least not by Hollywood's standards.