While Star's sneaky, I'm not sure it's intelligence. She tends to avoid trouble because she's the first to run, but she's also the type to lose focus on her task and wander off, which is why she's the first to run. Sunny seems like she has the most competence, although that might be because she seems to have the most useful power and so uses it more.
>ternity is probably the only fairy we've seen that seems genuinely intelligent and understands when to avoid picking a fight with people.
That's not really a good measure. Even the three fairies know not to mess around and make Reimu or someone mad without being able to get away. In fact, what you're referencing is just her telling Clownpiece not to set fire to the shrine yet again, something the three fairies have told her not to do too, so she's smarter than Clownpiece yet again. (Provided Clownpiece is the only fairy that can read/speak two languages).