I wasn't a big fan of the diplomatic favor (is that what it was called?) in VI, but I kinda think that the influence in VII can be pretty neat. I had a pretty tough time in my most recent game. I was staying out of alliances, but eventually I got declared upon by two civs, that snowballed into two more the following turn. And I like that influence here can be used as an additional weapon, and the AI did pretty well in keeping the pressure up. Gengis wrecked me through war support, and my closest neighbour kept sanctioning me. I couldn't defend against it all, and it turned into a really fun defensive war on several fronts.
The closest neighbour was definitely the "sanction-happy" one in this particular game. I actually had a good relationship with them at the start, but I ruined that, which came back to bite me later.
All these systems have a ways to go I think, but the war and how it proceeded felt pretty "dynamic" for lack of a better word.