This really depends on where you live. Harassing and other similar situations are very common in Taxis where I live, while Uber drivers seem to be well-behaved.
None of my female friends dare get into a Taxi due to, well, harassment, (some have stories of groping, attempted rapes, etc.). Generally, they'd only take a taxi in groups, or walk.
Uber seems to be working well in that regard (at least for now).
In my country, Uber service is far better than taxis by a mile... many taxi drivers are poorly-paid employees which don't care much, and they're basically immune to any kind of incentive or threat.
On the other hand, Uber drivers with a bad score are usually suspended or banned from the app, keeping out the bad apples, and they're usually the car owners themselves, thus having an incentive to drive better and take more rides.
I believe than something similar to Uber scores for taxis with similar effects (removing bad drivers from the service) would create a huge improvement.
Another unfortunate side effect is that there's some segmentation - poorer and older people still take taxis, while more affluent people take Ubers.
None of my female friends dare get into a Taxi due to, well, harassment, (some have stories of groping, attempted rapes, etc.). Generally, they'd only take a taxi in groups, or walk. Uber seems to be working well in that regard (at least for now).