How close to the real thing?

If memory serves, the late Peter Walker (Quad) answered to such a question- about 15%.

An old trick, often used at shows, such as CES. Go near some expensive demo
and throw some spare change up in the air. When it hits the ground heads will really turn. Reality is so much more complex than any reproduction.

I have flown through the Gand Canyon in a helicopter, and I have seen Imax. I have also tried memory experiments and read books about how recall works. The texture of simulation is far removed from real sensory experience and memory is but a type of simulation.
What all simulations share is distortion and lack of information. One day we might achieve near perfect reproduction of a recording, but no chance ever of reproducing the "experience". I imagine a time when a person's reaction to an event can be recorded and "played back" through direct brain stimulation, but the rules would still apply.
Finally there is the novelty phenomenon. An ad for an early Edison record player shows an Opera singer listening to a recording of another singer with his eyes closed. He witnesses that he cannot tell any difference from hearing her live. We chuckle, but I expect he really was thrilled and enchanted with the novelty, so he was easily fooled.

Atmasphere, as usual, has something to say. Those of us who play an instrument which can be amplified (classical guitar), know that even cheap mikes and speakers can sound more "real" than any recording. The storage systems are the most destructive to the sound. That said, I think much of the disagreement comes from the type of music considered, and its venue. I have performed on stage (I sing tenor) with huge orchestras, pipe organs, and in the case of some memorable Russian music, with an extra large percussion section. Even though the din got so loud at times that I could not hear my own voice- and a fraction of a second later all was full stop but for a single voice, yet there was never any sense of strain or was there difficulty in hearing the soloist.
It has been observed by some cynics that a group of musicians can sound exactly like a loudspeaker, but not vice versa.

Yes, removing the room signature with digital equalization is a most promising technology. I have used the Tact system for years. Goes without saying that it is a work in progress, but a little recognized benefit is the lowering of the noise floor. Tubes are great, but they are noisy compared to digital amplification, and that noise obscures quite a bit of detail. I hasten to say that digital amplification is far from perfect, just saying that it does some eye opening things right.