stoneinapond
Veteran
You did get an answer but perhaps it was unclear.
Sound for video is a complex question. We hear things in different ways than we see the world, although obviously they do intersect a lot. Our ears are in some ways omnidirectional, but also very directional when required, like picking out a conversation in a crowded room.
However, microphones behave differently from our ears. If you used a stereo microphone in a crowded room it would be very difficult to isolate that conversation, but you would capture the sense of "space" that stereo provides. If you used a mono shotgun, then you would be better able to isolate the conversation but would loose the sense of the space. It doesn't mean it's not there, but the 3D-ness of the sound stage would be flattened.
I could go on and on, but to your very specific questions here, you will have problems catching clear birdsong with a stereo microphone unless you stuck it up the bird's beak (I jest but I'm trying to make a point here.) So you would want to use a mono shotgun in that case because that has more "reach". Now don't go thinking that a shotgun is the equivalent of a zoom lens. It doesn't bring the sound closer, but by eliminating (attenuating) the surrounding sound you get a perception of loudness. You can also bring that clip up in post for that reason.
Now if you want the ambience of a fair, perhaps a stereo microphone would be better since you a capturing sound that is a little closer to what the ears hear when they are not focusing on a particular source. The issue here is, that if you have the microphone on the camera, as you pan, so does the "soundstage" in a more distinct way than what the ears would hear in the same situation. Which may or may not be what you want. You need to experiment there to understand what I mean.
The rule of thumb, if there is one, is that for sources that you want to isolate, you use a mono microphone. You then add a sense of ambience in post if you want to mix that with stereo sound. The sense of ambience in these situations are generally second microphones or takes that are recorded later (called atmos) and then blended in with the original. But care needs to be taken because our ears aren't fooled as easily as our eyes. Any obvious disconnect between the visuals and the audio will immediately throw the audience out of the illusion.
Well, I did go on and I hope I didn't confuse you. There is no simple answer to your dilemma, which is why production and post audio are issues that require separate attention.