I don't like when maps clearly show their grids/lines in their art (where, for example, even natural settings have orthogonal orientations). Aesthetically, I prefer natural and realistic layout, even if the style is anime or abstract (rather than true realism).
With that said, if the gameplay and movement are taking place in a grid, then the map shouldn't be so "natural" or jagged that the player cannot tell where they can and cannot move. It's possible (and ideal) to fit a natural map to a playable grid. But short of that, it's probably better to have an orthogonal aesthetic than it is to have a natural map which doesn't reflect the actual playable area that well.