I don't think I have ever heard the quartet before, but they are very fine players, highly skilled technically, with superb ensemble and a high degree of expressive intensity. There is a good-quality clip of them playing the third and last movement of the Bartók on YouTube:
There does not seem to be a clip of the Parker Quartet playing the Schubert on YouTube, but here is a fine performance by the Emerson Quartet:
Even at this fairly early stage of their career, the Parker Quartet seem to have established themselves at the highest ranks in the string quartet world. They are superbly accomplished and don't seem to fall prey to the latest fashions, meaning that they don't bore us with long talky introductions and they don't pander to us by playing tangos for encores. They even play Shostakovich, one of my favorite quartet composers. Here is a performance of the Quartet No. 9 at the Library of Congress three years ago. Notice that they have changed the seating since this concert. The viola is now on the far right.