this is difficult to generalize. Which wear rate fits bets depends from the application. Same accounts for wear depth or wear volume. Maybe you can describe the application in more detail? If you can calculate both I would recommend to compare with literature or in best case with experimental results.
although there are many profilometry techniques that successfully measures the wear depths or wear volume, optical profilometry using interferometery techniques are more accurate to gather the surface topographical informations.
Considering that wear depth can vary significantly, it is not the best parameter to generally describe wear loss. However, depending on the specific application it might be useful. For example, when it comes to coated samples, wear depth can reveal weather the coating was completely worn off.
Sometimes, neither wear depth nor volume loss are appropriate. For example, when wear tests are conducted with different loads. It might be often found that wear depth and/or volume loss obtained for different loads are directly compared, which is wrong. Usually, wear loss is higher for higher loads. Here it would be more appropriate to calculate wear rate.