This is a tough choice - I dearly loved both shows. For what it's worth, I think I loved Caroline just a bit more, and I think the score is genius. But that's just one opinion, obviously.
Here are a couple other factors to considers -
1. From the direction of this thread, it may seem like Caroline is the more divisive of the 2 shows. But worth noting that North Country is also quite divisive. Some people don't vibe with its loose plot structure, and its mood-driven approach to musical storytelling (when I first saw it at the Public, I compared it to shows like "Once" and "Band's Visit" in terms of the tone and pacing). Some people find it too boring and messy. Caroline, by contrast, is a bit more traditional as a piece of musical theatre. So that may come down to personal taste.
2.. North Country is directed and written by the same person - and it's a pretty direction-driven show. So this original production is likely to be the best production of the show we ever see, or at the very least, the most closely aligned with the intended vision for the material. Caroline, on the other hand, will likely be revived again someday and/or produced regionally. And when that happens, it could very well be just as good as the current Broadway production.
