Source for notes: The String Quartet, A History by Paul Griffiths, Thames and Hudson 1983.

1. The composer most influenced by the quartets of Haydn  (and particularly the op.33) was Johann Chrysostom Wolfgang Amadeus Mozart (1756-1791).
2. The 26 string quartets of Mozart may be divided into two basic groups: the 16 written between 1770-73 (K.s' 80, 136-138, 155-160, and 168-173) and the 10 quartets composted in 1782-90, consisting of the 6 dedicated to Haydn (listed below), one dedicated to F.A.Hoffmeister K.499, and the so-called Prussian quartets (K.575,589, and K.590).
3. Of the early quartets of Mozart, (1770-73) 10 are three movement works in an Italian style.
4. The quartets K.168-173 (pre-1773) are Viennese in style and reflect Mozart's acquaintance with Haydn's op.17 and op.20 quartets. Each of these Mozart works has four movements, including a Minuet. There is considerable use of counterpoint, resulting in greater independence of parts and more importance accorded the three lower instruments. K.168 and K.173 have fugal last movements.
5. There are written records of the two composers participating in performances of the Haydn op.33 together. Although likely apocryphal, the story goes that Haydn and von Dittersdorf played the violins, Mozart the viola (his favorite) and Vanhal the Cello. If this is true then their impact upon him is all the easier to understand.
6. Mozart responded by beginning his Haydn Quartets in 1782. They are 1. K.387 G major, 2. K.421 D minor, 3. K.428 Eb major, K.464 A major, and K.465 C major. They were published in Austria as his op.10 in 1785 and dedicated to Haydn and in Mozart's own handwriting declared to
be "the fruits of long and laborious endeavour".
7. The fact that Mozart spent two years on these 6 works (as compared to 6 weeks for the last three symphonies 39, 40, and 41) is testament enough to the care he lavished upon them.
8. There are two homages in these works - a Minuet in the Eb quartet which mirrors Haydn's in the same key, and the final variations of the D minor which reinterpret the theme of the G major variations at the end of the Haydn op.33 #5.
9. The new way of counterpoint that Haydn had initiated in the op.33, a freer treatment with less and less reliance on old contrapuntal devices, with a true conversational style wherein the melody becomes transformed by the various quartet members as they pick up the line, is borne out with complete dedication in these six quartets of Mozart. They are some of the finest examples of his genius. They are models of restraint and subtlety, and more chromatic than his other works of the period and in general with some notable exceptions (the G minor Symphony #40 and the Requiem).
10. The K.465 in C major, known famously as 'the dissonant quartet' is celebrated for it's introductory passage which inspired the name. Extreme harmonic uncertainty which contrasts so vividly with the brilliant, most Haydn-like C major allegro which follows, possibly finds its source in the 'wrong key' predilictions of Haydn.
11.While it is very difficult to discover the exact influence, Mozart imitated his mentor's methods of thematic presentation. Haydn's method was to take an idea and develop it into a large paragraph or even an entire movement. Mozart's was to juxtapose deeply contrasting ideas at both the level of phrase and paragraph. While this may seem more contradictory than similar, it is in the handling of thematic material with such flexibility and continued nuance that links the two composers.
12. This new polyphony of equal but different partners was the great advance of Haydn's op.33 and Mozart's 'Haydn' Quartets, and had far-reaching consequences not just for the string quartet but for the whole nature of musical composition in allowing composers to deal with parts that are, as stated, equal but different.