Quick Sort vs Radix Sort
This depends... If the number of input numbers is $n$, assuming the word-ram model of computation, a word size of $\Theta(\log n)$ bits, and worst-case inputs:


Radix sort would require $O(n \log n)$  time and $O(n)$ auxiliary space.
Quicksort with fixed or random pivot selection would require $O(n^2)$ worst-case time and $O(\log n)$ auxiliary space.
Mergesort requires $O(n \log n)$ time and $O(n)$ auxiliary space.


Radix sort and Merge sort are then equivalent in this setting.

Notice that using quicksort with random pivoit selection results in a time complexity of $O(n \log n)$ with high probability. Selecting the pivot deterministically in a way that partitions the elements into two sets whose cardinalities are at most a constant factor apart gives your an algorithm with worst-case time complexity of $O(n \log n)$ and $O(\log n)$ auxiliary space.