For myself, a significant difference is that writing a single word longhand "feels like" a single long unified action whereas typing a word "feels like" several short distinct actions. The motor-sensory action of writing matches that of speaking a bit more closely than typing, especially if you're a scribbler. OTOH I suspect typing is better cognitively for transcriptions, meeting minutes, etc., where deep understanding is unnecessary. I am sure you can cook up a study that proves or negates any one of these suspicions.

Sometimes I get benefit taking notes on a computer, e.g. I read Wittgenstein with notes in org-mode, took lots of notes about software/CS directly in the comments of the program implementing the ideas, etc etc.