The equivalence is "local only". Meaning that if you take a small volume of space, and measure first order effects, it is equivalent. But over larger volumes

The equivalence is "local only". Meaning that if you take a small volume of space, and measure first order effects, it is equivalent. But over larger volumes of space, there can be second order differences. An example of that is "curvature". Once you get to experiments involving the geometry of a black hole, you're a long ways away from the local equivalence, and it is no surprise that you can tell that something massive is nearby.