Between the two you've shared, I prefer the first one with hatching only, but that could be because there's no white in the second one, so the whole thing reads as dark. Also, the flats are, well, flat. I think there could be more variation within each character.
I don't have a ton of black ink experience, but one (analog) approach I learned from an urban sketching book by Gabi Campanario (@gabicampanario on Insta), was to:
1- lay down a light ink wash everywhere that wasn't meant to be full white highlights
2- layer that same light wash to create some shadows
3- layer a darker wash to emphasize very dark shadows
4- finish with some light hatching to describe the shape of forms a bit more
That's just one approach (which could be done digitally too), and maybe that way of thinking could be helpful to you.
Also check out Alfredo Cáceres (@redolaf on Insta). A lot of his work has color, but throw a black and white filter on them and you can see how hatching and washes can interact.