A wire lifts from underneath, which is why an underwire holds a shape that a knit cannot, and why it has to be the right band size before anything else works. A wireless bra builds shape out of the fabric instead, so it forgives a size in between and stops being a thing you notice at hour eight — and gives up some lift to do it. Buy the underwire when the top is close-fitting and the line matters. Buy the wireless when the day is long and nothing is going to be looking at your silhouette.
The wire is not the thing that hurts
A wire that digs is nearly always a band that is too big, riding up at the back and pushing the wire somewhere it was not designed to sit. Going wireless fixes the symptom and leaves the cause. If a wire has hurt every time, the next thing to change is the band size, not the category.
Most people want one of each
These are not rivals so much as a weekday and a weekend. The reason to know the difference is so that the drawer holds the right one for the morning rather than one compromise for every morning.