If you use Hoare's original select
algorithm, you can get the same sort of poor worst case performance that you can from Quicksort.
If you use the median of medians, then you limit the worst case, at the expense of being slower in most typical cases.
You could use the median of medians to find a pivot for Quicksort, which would have roughly the same effect--limit the worst case, at the expense of being slower in most cases.
Of course, for the sort (in general) each partition operation is O(N), and you expect to do about log(N) partition operations, so you get approximately O(N log N) overall complexity.
With median finding, you also expect to do approximately O(log N) steps, but you only consider the partition from the previous step that can include the median (or quartile, etc. that you care about). You expect the sizes of those partitions to divide by (approximately) two at every step, rather than always having to partition the entire input, so you end up with approximately O(N) complexity instead of O(N log N) overall.
[Note that throughout this, I'm sort of abusing big-O notation to represent expected complexity whereas big-O is really supposed to represent the upper-bound (i.e., worst-case) complexity.]