Important fact is that burst sort ("string" being the important keyword in title) is not as general as quick sort and thus it can be very fast. With assumptions required by quick sort (having comparison operator) sorting cannot be faster than O(Nlog(N)) (on average).
If you are interested in general sorting algorithm with good worst case performance, try merge sort. Merge sort is O(Nlog(N)) independent of input data, but with significantly larger constants than quick sort, also in theory it requires O(N) auxiliary space, but that is only case for arrays, linked-lists can be sorted in place.
Smooth sort is better than mergesort, offering in-place sort that approaches O(n) as the data approaches sortedness (lower bound is O(nlogn)). It is, however, very complex to implement.
If you are interested in general sorting algorithm with good worst case performance, try merge sort. Merge sort is O(Nlog(N)) independent of input data, but with significantly larger constants than quick sort, also in theory it requires O(N) auxiliary space, but that is only case for arrays, linked-lists can be sorted in place.