Good but not truly great, playing style is affected and overly sentimental
These are good performances, but are far from the greatest. Perlman is a fantastic violinist without question; he can play anything he wants to, and do it flawlessly. Just listen to him whip through Paganini's caprices like it's a walk in the park. Ashkenazy is a fine pianist and able collaborator, even if he isn't my favorite. However, this recording is a bit over-the-top in terms of the schmaltz-factor. The music is already sufficiently heartfelt, and does not require any additional help from the performers to drive this point home. The playing style, likewise, is a bit affected and self-conscious.
Anyways, enough negative stuff. The 3 sonatas are played remarkably well, with a great deal of virtuosity, perfect intonation and excellent collaboration throughout. I may not LIKE the way they play, but I cannot deny the technical mastery of these works from the musicians displayed on this disc. Those that enjoy the use of portamento (and slightly excessive rubato) will thoroughly enjoy these readings. For me, my personal favorite renditions of the sonatas are Suk/Katchen on Decca Originals and Schneiderhan/Seeman on DG Originals. Suk and Katchen give a relaxed reading on par with this disc in terms of tempi, but with a more straightforward reading (Suk was well-schooled in the Brahmsian school, being related to Brahms' close friend Dvorak, and features a robust, slightly rosiny tone consistent with the Czech school of violin playing). The Schneiderhan-Seeman collaboration is a relentless, intense reading featuring quicker tempos than either of the aforementioned sets, and a steely, iron-fisted and thoroughly Germanic interpretation from violinist Schneiderhan, and is my absolute favorite. In my opinion this set most closely matches the music.
In all...a very good CD, and a fine choice, but there are better sets available. You should get all 3 discs if your budget can handle it.

CD
Brahms Violin Sonatas with Perlman and Ashkenazy is totally wicked! One of the best recordings available. HIGHLY recommended!

Difficult Choice
I have always preferred the Suk/Katchen rendering above all others. I've always enjoyed Perlman (and Ashkenazy, for that matter) until sometime around the mid 80's, when he drastically changed his playing style. But, somehow, I had never aquired this recording. I'm very glad that I finally did because it's pretty close to Suk's equal. You can't go wrong with either one (however, I think the Suk is now out of print), so my advice is to own both.

Brahms Violin Sonatas at their Best!
I feel pity for any pianist who accompanies Mr. Perlman, regardless how famous s/he is. After one hears Mr. Perlman's violin talking, whispering, begging, pleading, crying, singing, and pouring passion and love, one wonders why any other musical instruments are really necessary. It is often said that a violin is like a human voice. Perhaps it is so. But, please tell me of any singers who can match, even remotely, the heavenly sound of Mr. Perlman's violin!
I listened to this recording several times. After I have somewhat satisfied my hunger for Mr. Perlman's playing, I focused on the piano part. One would think that the sheer volume of the piano chords would supplement the violin part. I was mesmerized to find out that in several instances Mr. Perlman's single note can match in volume, beauty, expression and the tone color an entire chord by piano. There were, however, some really nice parts for the piano, which Mr. Ashkenazy played superbly. These Brahms sonatas are very nice and interested pieces, and I promised myself to listen to more Brahms in the future.
I most highly recommend this recording.

A Great Recording of the Century
This is music-making of the highest order - the freedom and unanimity of interpretation you hear when two great musicians who love to play together take their time to work on details of tempo changes and phrasing. The performance is elegant, unhurried, Brahmsian; expressive but not sentimental.
It may be an artifact of older technology or maybe the recording engineer didn't get the balance right, but as another reviewer said, the violin sounds too loud. Ashkenazy plays with restraint when called for, and you can hear him - especially when he needs to be heard - but this is Brahms after all, and the gorgeous piano part is not a mere accompaniment. All in all, this is a fantastic bargain! Buy this recording!