1. Both predict the same critical radius, now called the Schwarzschild radius.
2. Both predict a central singularity with formally infinite density in idealised collapse.
3. Both predict exactly the same finite time to fall into the singularity under equivalent idealised conditions.
4. Both give the same equation for radial free fall, using different definitions of time.
What GR added was meaning to these things (and of course precise calculations outside of very idealised scenarios and symmetric conditions).
In relativity the event horizon really is a point of no return, whereas in Newtonian physics it's the point at which escape velocity is equal to the speed of light. The escape velocity on the surface of the Earth is 11 km/s, but that doesn't mean that I as a human can't escape the surface of the Earth momentarily just by jumping and I certainly don't jump 11 km/s or even 1 km/s for that matter.
Similarly in Newtonian gravity it would be possible for an object to enter the event horizon of a black hole, and then "jump" back out at a much lower speed than the speed of light and then get sucked back beyond the event horizon, and you can in principle do this over and over again so long as you had some sufficiently powerful source of thrust.
In general relativity this is in principle not possible.
Which is why the concept existed long long before any talk of relativity or time dilation, back before anyone knew the name Einstein. (He was like 4yo when this came out)
From American Physical Society: "the true “father” of the black hole concept was a humble 18th century English rector named John Michell–a man so far ahead of his scientific contemporaries that his ideas languished in obscurity, until they were re-invented more than a century later."
https://www.aps.org/apsnews/2009/11/1783-john-michell-black-...
I thought you need at least special relativity for time dilution.