I keep a work journal in markdown on the computer. Like you said, it has the benefit of being easily searched.

I also keep a personal journal that I write in more freely once a week. I don't have the "search" requirement there. Reading and writing with pen and paper is more soothing to me for whatever reason. I do like the freedom of pen on paper when compared to typing. I can quickly sketch out a graph or diagram for example.

Each has its benefits and drawbacks. Use what fits your use case best :)