The best place to look for new data where we might find reality disagreeing with either model is in the extreme parts of the universe, like black holes. If there was even a hint in this photo that General Relativity wasn't perfectly accurate, we might be able to take the discrepancy and build a new model that solves the disagreement.
Whoever does that gets a Nobel Prize and has their name as immortalized as "Einstein".
The fact that general relativity continues to hold up to every observation we can make is remarkable.
Granted, I only ever got as far as E&M physics in college so I could be way off here but that scenario has turned up so many times in history.
This is a semantic nitpick, but I don’t think it’s useful to think of these theories as “wrong”. They are both models that make predictions about physical phenomena that, when tested, are extremely accurate. They provide incomplete and inconsistent predictions of what happens at the very edges of physical reality, and they need reconciled.
It might just not be possible to see anything odd without having a black hole right there to study, but there’s always hope that the next new observation will provide a clue as the previous ones repeatedly have not.
https://gizmodo.com/why-cant-einstein-and-quantum-mechanics-...
https://www.theguardian.com/news/2015/nov/04/relativity-quan...
https://en.wikipedia.org/wiki/Problem_of_time
https://physics.stackexchange.com/questions/387/a-list-of-in...
For a good general source if you want to learn a lot more from a good popular science point of view (but one that takes great care to not accidentally mislead by oversimplification as often happens with popular science) about general relativity and quantum mechanics, try PBS Space Time, especially after Dr. Matt O'Dowd took over as host and main writer.
I'll add an additional recommendation: Stephen Hawking - The Theory Of Everything
https://www.quantamagazine.org/where-do-space-time-and-gravi...
Black holes are a solution to the general relativity equations, but Einstein thought they were just a mathematical quirk, and that in real life, they wouldn't have been able to form.
So ever time someone says "Einstein was right" when talking about black holes, then no. He was right about general relativity, but he was wrong about the existence of black holes.
You wouldn't be surprised if your door opened just as usual when you put your key in the lock. The day it starts jamming however, you get very interested.