Merge sort uses a divide and conquer strategy that divides the array into halves and recursively sorts the subarrays, then merges the sorted halves back together. It has a time complexity of O(n log n) as it divides the problem space in half on each recursive call until reaching base cases of single elements arrays. Compared to quicksort, merge sort uses more space (O(n)) for an auxiliary array but has a guaranteed O(n log n) worst case running time versus quicksort's average case of O(n log n) but potential O(n^2) worst case.