I take trains and subways whenever in NY/NJ and have never had a scary or threatening incident. Some minor annoyances, yes, like when people come begging through the cars, but I copy the other riders and simply avert my eyes until the offenders move on to the next car. But threatening? No. That said, I keep my wits about me, don't make myself an appealing target by flashing cash or expensive jewelry, and keep to well populated areas wherever I travel.
The article about London subways refers to crime statistics from Nov 2015-Oct 2016 (1,980 reported incidents) versus Nov 2017-Sept 2018 (2,838).
I learned from Hans Rosling's powerful book "Factfulness" that when looking at statistics, context is king. How safe are people in cars, buses, planes, subways and other modes of transportation per mile traveled or per trip, for instance.
In this case, the Guardian article cited states that over 11 million passengers use London Transport per day. Given that context, fewer than 3,000 incidents for the entire year seems quite safe to me.