Panel models are popular models in applied sciences and the question of spatial errors has recently created the demand for spatial system estimation of panel models. In this paper we propose new diagnostic methods to explore if and how the spatial components will make significant differences of spatial estimates from non-spatial estimates of seemingly unrelated regression (SUR) systems. We apply a local sensitivity approach to study the behavior of spatial ordinary or generalized least-squares estimators in two spatial SUR system models: a spatial autoregressive regression model with SUR errors and a SUR model with spatial errors. Using matrix differential calculus we establish a sensitivity matrix for the spatial panel models. We show how a first-order Taylor approximation based on the non-spatial ordinary or generalized least-squares estimators can be used to approximate the least-squares estimators in spatial SUR models. In a simulation study we examine the approximation results and demonstrate their quality. We also try to find whether the SUR variance or the neighbourhood weight matrix has more impact on the estimates and their approximations.