I'd say varying circling minima can be due to a number of obstacle and/or navaid constraints. There are limits to the gradients allowed for different sections of the approach so an obstacle from one direction on final could impose a limit that doesn't occur from another direction. MDA has to allow for the missed approach gradient so an obstacle could intrude into one runway's missed approach but not into another's.
Approach type could make a difference too. Different approaches have to consider different tolerances leading to different obstacle considerations.