They both operate in the same way - connecting two contradictory ideas in a sentence. There are a couple of differences.
'Although' connects two unequal ideas and indicates some measure of surprise.
"Although it was long, we enjoyed the movie."
"The movie was long, but we enjoyed it."
The difference is that I can flip the phrases in the sentence with 'but':
"We enjoyed the movie, but it was quite long."
"Although we enjoyed the movie, it was quite long." - doesn't make as much sense.
Note that 'but' does not occur in the first subordinate phrase, while 'although' can occur in two places.
I can't flip the phrases with 'although'.