I had the Berkeley for a good long while, using it with a computer configured as a music server and a Lynx sound card. It was a great DAC, and improved a significant notch with the addition of the Straightwire Info-Link cable in place of the Lynx cable. In my opinion, if you are using the Berkeley with a Lynx sound card, the Straightwire is a no-brainer upgrade.
In my system, the Berkeley was incredibly dynamic, with an excellent sound stage and startling clarity. It was the best digital I've ever had in my system by a good margin, and I heard it in direct comparison to several excellent digital players.
With that said, I tried and bought the Weiss DAC202, which is equally dynamic, but more organic than the Berkeley. In my system and to my ears, it is more analog than the Berkeley--which is not to challenge Suteetat's viewpoint as much as to stress how important it is to hear these DACs in your own system if possible.
I would say the Berkeley is the best digital I've heard, but only because the Weiss is the least "digital sounding" player I've heard. Both are great DACs, but in my system and for my preferences, the 202 is on another level.
I have no experience with the Ayre. I think you would likely be very pleased with either the Berkeley or the Weiss.