Both methods in Hierarchical clustering have always the same result (number of clusters and instances in the same clusters) and the difference is only the way they use to compute the result? Or the result can be difference (in terms of instances in the clusters, in agglomerative and divisive clustering)
Except for single-linkage the results can be very different.
It's easy to see that the tree found by hierarchical clustering cannot be optimal at all levels. Top-down will be good at the first level, then degrade. Bottom-up will be good at the first merges, then degrade.