Why are both Schrader and Presta valves still used on tubes?
The main thing is that the Presta valve is thinner, and takes less of a bite out of the rim.  This is quite important as the rims get narrower.

Further, the Presta works better with hand pumps in that there's no spring that the pump needs to overcome to get air into the tire.  Also, the Presta always has the fully-threaded body (which is possible with Schrader, but rare), so a nut can be used to hold the valve in place -- again, quite important with hand pumps.

Never had a bike valve stem break on me, that I can recall.