The best thing (to me) about Neighborhood Stories is being able to turn it completely off if one doesn't want it, and being able to customize it if one does want it. As @cyncie said, it's definitely easier to customize, but I personally prefer the broader and finer amount of control I can get with MCCC. However, it does require learning what does what (and what doesn't do what). It can be aggressive, but it doesn't have to be.
For example, in most of my saves I don't use the moving in/out settings on a regular basis, but whenever I do (for occasional purposes in some saves), I can fine-tune them to my own preferences. I also don't let MCCC handle marriages (or other relationships) on a regular basis. I do let it handle random pregnancies, but the pregnancy chance percentages are low enough to prevent it getting out of hand while also being high enough to keep my saves populated. I also don't allow them to be completely random; my settings are based on whether or not the sims chosen for potential pregnancy have ever woohoo'd together. Sims in romantic relationships, whether it be BF/GF or other SO types, engaged couples, or married couples, are considered by MCCC to have woohoo'd at least once, whether or not they actually did. That's still better than the game picking random couples without regard to their sexual preferences or without their ever having met.
If you have no interest in experimenting to find your own best settings to suit your style with MCCC, I'd definitely recommend experimenting with Neighborhood Stories instead. Assuming you do enjoy at least some of the elements of "story progression" in the first place, of course. :)
