Anyone who has ever heard Mr. Barenboim conduct an orchestra, be it the Chicago Symphony Orchestra or the Berliner Philharmoniker knows that Barnboim is one of the most talented interpeter of our time if not The most.
However, I say to you that if you haven't heard him play Mozart you are definitely missing out. I always thought that Horowitz understood the Mozart sonatas best. He conveyed the "understanding" of the music without sentimentality. Perahia gives his regular performance - perfect and dull and Uchida plays them as the most skilled pianist can play a piece whose notes he only received moments earlier.
I can't describe how Barenboim plays Mozart - he makes those Sonatas linger in your stomach, surround your ears and draws the music into your soul, without ever coming close to over-sentimentality. Those sonatas are simply... more beautiful when Barenboim plays them. I'm sure if a computer comapred the timing of the keystrokes between Barenboim and Horowitz it'd find almost no difference at all - but Barenboim simply makes me FEEL better with the music.
If you've got no other performances of the Sonatas, I recommend you start with these. Anything else out there is certainly not better, it can only come close to this performance.
And while we're at it you'd do well by yourself if you get Barenboim conducting Mozart's Requiem - i've got 10 different performances of the Requiem - all of them have something i really like about them, and a few things i rather be different - but Barenboim's performance (with some french orchetra & choir, i don't remember) is flawless and brilliant in the conductor's understanding of the music, and the orchestra and choir's performance is impeccable under Barenboim.