From what I've seen, most people don't actually perceive a huge difference, and either only know about one, or use both indifferently. That's to be expected, because a huge percentage of Reddit users in general only come on the site to consume content, and don't think too critically about the moderation styles and communities of the subs they join as long as they put interesting things in their feed. Of course, few of them will comment in this thread, so you might not realize that's the majority.

Of the people that do have a preference one way or another, I've observed that r/nyc users think r/newyorkcity is over-moderated by extremely liberal mods. r/newyorkcity users think r/nyc is full of conservatives and is, depending on who you ask, under-moderated or over-moderated by conservative mods.

I use both, although not indifferently. A case could be made that r/newyorkcity is slightly more left-leaning and more strongly moderated, but both reflect the variety of political views you find in the city to some extent. There is one clear difference, though: r/newyorkcity users are significantly more likley to have a strong opinion on r/nyc than the other way around, as you've probably observed by now.

I'd recommend using both as well. I'll save my rant about the two party system for a more relevant thread, but I will say that people in the city are much more likley to pick and choose which parts of a given party's platform they subscribe to than people in other parts of the country are, so you shouldn't assume you're "surrounded by trumpies" just because somebody voices one tough on crime opinion.