The whole set is of a great music. His melody are introvert, not many catchy movement but many starts with slow movement with extra care and solid build up of melody. I really like the 11th quartet where the 3rd movement , Allegreto pensieroso shows his folk music inserted and haunting in this majestic piece.
The 13th maybe the most popular with also the 2nd movement, Presto Fantastico highlighting the whole piece and excellent Finale to the cycle.
Beside the cello and viola also got many upper melody and serve as something like a 'fugue' like arransement. According to some sources Myaskovsky has many German elements rather than Russian in this respect. The term 'lyricism' should be apply maximum to his quartets.
For a quick preview here the sample of Myaskovsky I can found on net, played by Stravinsky String Quartet , see his page here.
The Taneyev Quartet version is a precious gems, and if any other recent CD on Myaskovsky is the Borodin Quartet :
Then there is a newer 1st and 13th quartet recording by Renoir Quartet