1km / pixel is about the minimum that you'll need to get plausible results. You will probably want to overlap adjacent maps by at least 10% to get plausible erosion joins.

Erosion is a global problem and not particularly amenable to breaking into tiles because the edge conditions really matter, esepecially incoming flows from other areas. For the programmer pedants out there, yes, the system could break the large surface down into arbotrarily many smaller tiles, but it would still be treating the tiles as a single surface for the purposes of the operation.