In anaphase I, the spindle fibres from the opposite pole are attached to the two different chromosomes (on a single side of the chromosome) of a bivalent which leads to separation of chromosomes from bivalent whereas in anaphase II, the spindle fibres are attached to the single chromosome on both sides through the kinetochore on centromere which leads to separation of sister chromatids.
The other differences are: anaphase I is part of reductional division whereas anaphase II is part of equational division. Anaphase I changes the ploidy of the cell from diploid to haploid whereas anaphase II maintains ploidy of the cell.