This question covers the difference between でも and けど for "but", the difference being that でも can be used at the beginning of a sentence. But けど and が are used in very much the same way, syntactically. What exactly is the difference between these two expressions?
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By comparing these sentences, "けど" appears to be softer and more common in informal speaking. "が" delivers a sense that the speaker/writer is assertive, often used by a person in a higher position or in formal writing.
I think that が is disjunctive while けど is concessive. That is to say that が may connect two disjunctive (disconnected) parts, while けど not just connects the two but introduces the succeeding clause as a circumstance that might be expected to preclude the action of the main clause but does not.
I think the term "disjunctive" is a superset of "concessive". That is to say that "disjunctive" includes "consessive".