Are both of these sentences correct? Are there any subtle differences in the meaning conveyed?
If they are not entirely interchangeable, how do we know which one to use?
Both of them are correct, and the
They are almost the same, but if you do want to distinguish the meanings (except for the spoken/written difference):
Maybe that's not a very good example. But I cannot think of a better one because both of them are almost the same (99.9%). :p
Both sentences are grammatically correct and almost the same in meaning. Speaking of the slight difference, the first sentence (跟) is more of an oral language while the second (和) is kind of formal or written.
Both 和 and 跟 mean "with." In this regard, they are basically interchangeable.
Of the two, 和 is more formal. It is also the more "equal" of the two words.
跟 has the connotation of "following" or "tagging along" in order to be "with" someone. In Chinese society, that is actually more "acceptable," because you are being "agreeable," (as opposed to "proactive"). Meaning that many would find you the companion of choice.