Kip Thorne starts out Chapter 11 of BLACK HOLES AND TIME WARPS with that question.
I wondered what experts here might think of that within the context of the following:

The flat spacetime paradigm doesn't give you different predictions, than the curved spacetime paradigm. It is just a philosophical question: Is spacetime curved or is just every observable thing behaving as it was curved.

This good idea fails inside the BH horizon, where you have actually a separate (from the entire universe) flow of time. So it cant be explained by just time/space dilation.

Dimitry..according to Thorne they ARE mathematically equivalent...everywhere in everyway...that's why I posted it...In your example, gravitational lensing, the conventional "curved space" paradigm does seem a better approach...

AT has stated it precisely the way Thorne presents it...

Science doesn't answer questions like "is space really curved?". Theories don't tell us what something is like. They only tell us what the results of experiments will be (or more generally, what the probabilities of the possible results are, given the results of previous experiments). We can usually interpret a theory as describing what something really is like, but the only thing experiments can tell us is how accurate the predictions are.

It seems that in this case, we have an alternative theory's equivalent to GR, at least in the sense that it makes the same predictions about the results of experiments, but probably also in the sense that the axioms of either theory can be derived from the axioms of the other.

The alternative theory describes spacetime and measuring devices in a different way. We know that both of these descriptions are incorrect, since the theories don't include quantum phenomena, but let's forget about that for a moment and pretend that the universe is classical. Which description is correct? What could possibly answer that, if experiments can't? (Hint:)

Well, that's the question. Thorne indicates the theories are fully equivalent, and so does MTW. But is that right even down to admitting the same space of solutions?