I think there is no differences between both methods in animals and human, because they have the same concept that rate at which the RBCs or erythrocytes, in a sample of blood settle at the bottom. but the difference my be related to the time intervals for taking the reading of sedimentation rate.
Really there is no difference. I have wide experience of ESR studies of human, rat, hamster, ground squirrels and other erythrocytes, using spin probes for membrane components (both lipid and proteins) as well as a water-soluble TEMPONE for cytosole state and membrane barrier function studies. Very informative and express method, demanding minimal amount of sample.