At low speeds relative to the speed of light, they have the same accuracy don't they? And in that case, the Newton model is simpler so more useful. At high speeds, it becomes inaccurate and then you need the other model.
So there is no global "right" or "wrong", just different measures of usefulness depending the problem constraints.
> At low speeds relative to the speed of light, they have the same accuracy don't they?
GR is always more accurate, but the increased accuracy is not always needed; at low speeds relative to the speed of light the difference is often too small to matter in practical terms.
> At low speeds relative to the speed of light, they have the same accuracy don't they?
When measuring signal (ie radio, light, gravity) from slow speed perspectives, newtonian physics is not as accurate - https://futurism.com/newtonian-physics-vs-special-realtivity - Eg we actually need to account for it between gps sattelites and we do so from the perspective of GR as well as the recent evidence of gravity propogation being restricted to localization (ie roughly the speed of light)
Yup. And when you need to measure where artillery shells land, the GR model is overkill and you'll waste less time by using a Newtonian prediction. I think this proves my point?
"Newtonion physics is a perfectly acceptable approximation in many circumstances" and "GR is less wrong than Newtonion physics" are not in conflict. Newtonion physics can absolutely be "more wrong" and "useful in many circumstances" at the same time- and in fact is!
If your point is that they're both equally wrong, then no, I think you've disproven your own point. There are no circumstances in which Newtonian math produces better results than GR. That the latter is more complex is not relevant to the discussion of whether one is more accurate for a wider range of phenomena than the other.
Besides the valid points of the other commenters, I have a nitpick: It is special relativity that deals with things near the speed of light, you do not need GR for it. GR is necessary to account for strong gravitational fields.
Then why does GR make more accurate predictions?