I use my phone for quick notes on the go, or creating lists of information I want to be able to re order and edit.
I use pen and paper mainly for brain dumps. Getting a stream of thoughts out of my head and on to paper. I find trying to use a phone for this will lead to some distraction and the thought will go before I capture all of the info.
I also use pen and paper when studying a topic, especially for a test, I find the simple of act of writing the information down is enough to cement it in my brain, even if I never go back and read those notes.