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'classical' music is interesting in that there is almost always a distinction between the composer and the performer(s). One person writes a piece, a group of different people (conducted by another different person) perform it.
Compare that with modern music. A band/songwriter creates a piece, and they perform it. The composer and performer is usually the same person/people.
The main difference between these approaches is that, with the modern approach, there can be no debate as to the authenticity and credibility of the performance. The people who wrote it perform it, and very often have a studio recording of it. All these things provide for a very clear image of what the 'correct' version of this piece is.
In Mozart's time, all they had to go on was the notes on the score and any written/verbal instructions that the composer might have given. Any performance of such a piece, ever, is subjective, as the conductor and performers have to give their INTERPRETATION of what the composer has written/said. And very often, precocious conductors/performers would take liberties with these instructions and even disagree with them, thinking their own vision of how the piece should be performed to be superior. So yes, every recording of a classical work is a 'reconstruction' or interpretation and it is quite impossible to ascertain that the way in which one person/group performs it is the single 'correct' way. So yeah, every recording is (and sounds) different. It is impossible to say whether one is 'best' as this is a personal, subjective decision. One person's best could be another person's worst, and vice versa. Of course, some recordings could just be technically bad i.e. poor quality recording and/or musicians. There are groups who play on period instruments (i.e. instruments constructed to be identical to how they would have been during a certain musical period) and who aim to perform pieces from certain periods in an 'historically informed' way, i.e. having researched performance style etc. of the time. However, as modern listeners, we are used to a modern aesthetic and so it is not correct to say that, just because these performances might be historically accurate, they are the best. Pieces performed in a modern way might just sound 'better' or 'nicer' to modern ears.
>there were no high quality recording devices at the time?
There would have been no recording devices at all until at least 100 years after Mozart's time.