Grid and BSP

When partitioning the space with grids, there are some situations that obstacle would occupy half a cell. When using BSP, i wonder is it good to just partition the tiles that are partially occupied, and ignore the regular ones instead of partitioning right from the scene as a whole?
I do this because this way the pathfinder may generate "ugly" paths, also I am using cooperative pathfinding, if each tile varies in size, cooperative pathfinding is hard to accomplish.
Thanks
Jack