The R*-Tree is not just a different insertion leaf strategy.
The spitting strategy (perimeter!) is just as important, as it prefers "quadratic" pages, as opposed to the slices produced by other strategies such as Ang-Tan.
Furthermore, and this is maybe the key to getting prettier trees, the R*-tree performs a kind of rebalancing to actively avoid bad splits. Instead of splitting, when a node is overfull, it also removes the least central elements (or subtrees - you need this at all levels) and reinserts them. This doesn't always prevent the overflow, but it may reduce overlap in a tree.
But of course you can do various mistakes in implementing, and the R-tree will still work, just not perform well because of the bad structure. How bad is your tree, do you have a screenshot?