Why does Java's Arrays.sort method use two different sorting algorithms for different types?

The most likely reason: quicksort is not stable, i.e. equal entries can change their relative position during the sort; among other things, this means that if you sort an already sorted array, it may not stay unchanged.

Since primitive types have no identity (there is no way to distinguish two ints with the same value), this does not matter for them. But for reference types, it could cause problems for some applications. Therefore, a stable merge sort is used for those.

OTOH, a reason not to use the (guaranteed n*log(n)) stable merge sort for primitive types might be that it requires making a clone of the array. For reference types, where the referred objects usually take up far more memory than the array of references, this generally does not matter. But for primitive types, cloning the array outright doubles the memory usage.

According to Java 7 API docs cited in this answer, Arrays#Sort() for object arrays now uses TimSort, which is a hybrid of MergeSort and InsertionSort. On the other hand, Arrays#sort() for primitive arrays now uses Dual-Pivot QuickSort. These changes were implemented starting in Java SE 7.

One reason I can think of is that quicksort has a worst case time complexity of O(n^2) while mergesort retains worst case time of O(n log n). For object arrays there is a fair expectation that there will be multiple duplicate object references which is one case where quicksort does worst.

There is a decent visual comparison of various algorithms, pay particular attention to the right-most graph for different algorithms.