This is a difficult question to answer.It is easy for me to determine which one to use when I write because it feels right,however,it is difficult to explain.For you pure grammar academics out there,I have this to say to you:'But' is a coordination conjunction and 'Although' is a subordinating conjunction.But what do that meant to students of English?
1:both words are used to link 2 opposing ideas.
2:use 'but' if the contrasting sentence has a negative impact,or,the opposing clauses have equal importance.
3.use 'although' if the contrasting sentence is negative but acceptable - a positive impact,or,one of the opposing clause has a lesser value.
3.it is common to place 'although' at the beginning of a sentence with 2 opposing clauses,while it is more common to place 'but' in the middle of the sentence.
example:I accepted the job offer but the pay was low.(2 opposing clauses with equal value.I also gave the reader a sense that as soon as I can find a higher paying job,I would quit this one)
example:I accepted the job offer although the pay was low.(the 'low pay' in here is not as important as in the above example.I accepted this job despite of low pay and I did not give reader a sense that I would quit because of pay only.)