Alfred Einstein's book on Mozart, "Mozart, his Character, his Work" (Oxford University Press) is, in my view, one of the best written on the subject. I would like to share with you his (very interesting) thoughts and comments on the composer's piano sonatas.
Let's begin with the first sonata, in C major (K. 279):
"Mozart was a born pianist, while Haydn always thought in terms of the quartet or the orchestra. How often in Haydn's piano style one feels the translation from another instrumental sphere, while in Mozart everything flows smoothly under the hand. Thus it seems to me that the first sonata of the series, the one in C major (K. 279), must have been written before the "divagation". It gives the impression of an impovisation; the tones of the instrument sound in direct response to Mozart's imagination; this is how he must have played when he was in the vein and improvised a sonata. When other composers have displayed their ideas, one after the other, they repeat them in the recapitulation. But in this work nothing is mechanical; Mozart's fantasy is continually active in every detail. In the Andante, which is otherwise thouroughly Italian, this fact shows itself in the dynamics."
Here is Mozart's piano sonata K. 279, (not sure who the pianist is, but it's an excellent performance!):