Expensive optimization problems (EOPs) are becoming more and more ubiquitous nowadays. To effectively solve such problems, surrogate-assisted evolutionary algorithms (SAEAs) have been developed. Specifically, a SAEA usually maintains a surrogate model to simulate the real objective function of an EOP. Such a surrogate model is trained based on real-evaluated solutions. Then, it is utilized to evaluate the fitness of individuals in the EA instead of the real expensive fitness evaluation. Though many SAEAs have been designed, they mainly concentrate on dealing with low-dimensional EOPs with fewer than 300 dimensions. Their performance on large-scale EOPs with more than 300 dimensions is unknown. To fill this gap, this paper conducts a comparative study on two types of state-of-the-art SAEAs with a total of four algorithms on four classical EOPs. To make comprehensive comparisons, we range the dimension size from 50 to 1000. As far as we know, this is the first time to assess SAEAs on EOPs with such a wide range of dimension sizes and such high dimensionality. The comparison results show that the optimization performance of the compared four SAEAs on high-dimensional EOPs with more than 500 dimensions is not as satisfactory as their performance on low-dimensional EOPs because of their slow convergence. Therefore, research on large-scale SAEAs for high-dimensional EOPs still deserves intensive attention.