The AD738x has two Oversampling mode, Normal Averaging Oversampling and Rolling Average Oversampling.
Normal Averaging is best used in application where a high precision or high SNR or Dynamic range is needed and speed is not a concern, because it can average up to oversampling ratio of 32x but the tradeoff would is that it will have slower throughput rate as the oversampling ratio increases. On the other hand, the rolling average are best fit in application where both the high precision performance and throughput rate are desired. It can have a throughput rate up to 4MSPS and oversampling ratio up to 8x. Additionally in normal averaging the sampling instant of the additional samples is controlled internally by the AD7380. In rolling average the sampling instant is controlled by the user so for applications that are sensitive to the sampling instant rolling average oversampling mode would be more appropriate.