Based on the definitions you've used, I would say it's wayyyyyy more of a sandbox game. It seems to me, based on what I've seen, that the people who want to do machinima, write backstories, etc... in other words, make up stories they use the gameplay options to tell, are consistently the ones who are most happy with TS4. And everybody else has major ups and downs, or has left a long time ago.
That is, as it relates to gameplay. Obviously there are some people who get most enjoyment out of, like, build mode, and that's a whole other question in itself as to who and what it appeals to.
No matter what they tweak to make live mode more lively and in-depth, it seems to do a lot of annoying people or letting them down. And honestly, it may be the biggest reason is just the responsiveness issue that others have pointed out years ago. That with all the spammy idles and multitasking, sims aren't great at doing what you want them to do when you want them to do it, which when compounded over time, can kill flow if you're relying on the responsiveness of the simulation to keep you engaged. Whereas, if you're willing to make up stories to project onto the simulation, the responsiveness isn't as relevant. You need time to figure out where things are going in the story next anyway. At least, that has been my experience the few times I've tried a "make up stories" approach.