If you live in a congested city taking the train can be faster than Uber for some trips. I don't like paying $15-$20 for the privilege of sitting in traffic when the same trip would have cost me $2-$3 on public transit.
But there is a convenience factor to consider. Trains run on a schedule; they get crowded, you may have to stand; they depart from and arrive at predetermined locations. They may travel faster and more efficiently, but do they actually get you to your destination quicker? Do you spend effort planning your schedule around the train?
In my experience Uber is vastly superior than all other available transportation options.
In my experience it's only preferable to: 1. parking/driving downtown, which is more expensive and 2. not being late for work because I lack the will to get up some days. The express bus line here will pick me up reasonably close to my house and drops me off across the street from my building, and can drive in exclusive lanes, such that Uber/Lyft often takes longer and significantly more expensive. I do not live in a dense enough area to really care about how packed the bus is and I certainly don't care about whether I need to sit or stand.
In my experience Uber is vastly superior than all other available transportation options.