Java 6's Arrays.sort method uses Quicksort for arrays of primitives and merge sort for arrays of objects. I believe that most of time Quicksort is faster than merge sort and costs less memory. My experiments support that, although both algorithms are O(n log(n)). So why are different algorithms used 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.