Generally, gold ETFs should behave in the same way. For example, when one gold ETF accumulates gold, the other ETFs should do the same. However, sometimes it is not the case. Look at these two charts:

source: Simple Digressions

Note that in January the first gold ETF, IAU, accumulated 125.2 thousand ounces of gold (its total gold holdings increased by this amount of gold) but its much larger counterpart, GLD, decreased its holdings by 742.7 thousand ounces. 

Over the next months both ETFS were doing the same:

Interestingly, gold prices were going down or got stuck only in March, when both ETFs were selling gold.