Pros of pen and paper: always in my pocket, very fast to open up and read and write notes. Never runs out of battery. Readable even in brightest sunlight.
Cons of phone: must remember to take it with you or search your apartment to find where you place it and hope you have remembered to charge it during past couple of days. Additionally you have to unlock it and flick through the menus to find the note app. Additionally additionally you have to remember to take a charger where ever you go.