When I’m thinking and writing, I keep both readily at hand.
Handwriting slows me down and engages the creative part of my brain. Since handwriting is basically drawing letters, it’s a fundamentally different activity than typing and uses other circuits in your brain. I keep a notebook with unlined paper with me. I write and sketch in it.
Typing on the keyboard is much better at capturing my verbal brain in action. If I just need to capture words as though I am speaking, then the keyboard is what I need. I keep my Mac and iPad with me as well.
If I’m staring at a blank page using one method, I switch and try to break out of my rut. I find the back and forth helps keep the ideas flowing.