This set was my first exposure to Beethoven's string quartets, or Beethoven at all for that matter. Though these works initially struck me as very mysterious, with time and after having heard other recordings I have come to regard them as some of my favorite compositions of all time. Even (some might say `especially') in his last years Beethoven was brimming with creativity and these quartets are evidence of that. Movement after movement he expertly ties together a myriad of disparate ideas into these cohesive yet sprawling opuses of enduring appeal. They sound at the same time old and new - in his late period Beethoven took a renewed interest in Baroque music, while simultaneously emphasizing expressiveness and disregarding the constraints of conventional compositional forms. Thus he created a sound and style utterly unique and unequaled.
The Emerson String Quartet brings to these works a perfected ensemble as well as seemingly unlimited virtuosity. Coupled with the exceedingly clear and well balanced sound the result is a highly polished and perfectly played recording. Really, the only point of debate is the interpretations. Their approach emphasizes the drama and energy in the music, as evidenced by brisk tempos in the faster movements as well as strong phrasing and stark dynamic contrasts. Much of the music responds well to this approach. In particular I feel that the Emersons' take on Op. 132 and 135 are consistently excellent. Also, there are individual movements in the other quartets that are interpreted wonderfully - Op. 127 movs. 1 and 3, op. 130 movs. 1, 2, and 6 (both versions), and op. 131 movs 5,7.
Where I feel their approach sometimes stumbles is the slower movements. The relaxed, beautiful reveries of Op. 127 mov. 2 and op. 131 mov. 4, for example, are somehow not quite realized by the Emersons. These long variation movements benefit from grace, sensitivity, and subtlety. I only came to appreciate these movements after hearing the Alban Berg Quartett's versions. Curiously the Emersons do just fine in the glacial mov. 3 of op. 132, the `Song of Thanksgiving'.
I have read some people complaining that the Emersons sacrifice heart and expressiveness in their playing in favor of precision and virtuosity. On one hand I can understand how someone would say such a thing - the Emersons' playing is at times so perfect that it sounds nearly mechanical (see the presto of op. 131). They don't leave behind any of the foibles that some people find endearing in other recordings. But this music is inherently and unfailingly expressive when played well, as it is here. Other versions may sound more "human" than the Emersons' - whether that's a good thing or a bad thing is really up to you to decide. I think it's true that some groups add expressive touches to the music, and the Emersons are conservative in this respect.
Overall I think there this set has plenty to recommend to it, unless you've already determined that the Emersons' style is not to your taste. However, anyone who claims that this or any other cycle is "definitive" either hasn't listened to enough recordings or is being dishonest. No set completely captures the magic of this music. If you're a newcomer to the Beethoven quartets you should consider purchasing a set of the complete quartets. Note that there are many excellent cycles out there besides the Emersons', and that any ranking of these is really just a matter of personal preference. The Alban Berg set is a great and affordable choice, though some people take issue with the sound quality. I have also heard partial recordings of the Takacs and Cleveland quartets, which are excellent and notably expressive.
EDIT: For those considering this release I recommend considering the new budget release of the ESQ's complete set of Beethoven quartets (Beethoven: the String Quartets). It takes up less space on your shelf and only costs a little more. The middle quartets in particular are worth the extra dough, but the early quartets are given fine, dramatic readings as well. The only downside to the budget set is that the liner notes are pared down.