I don't know... I don't even know if this question can be answered, so feel free to ignore everything I say...
I'm an electronics engineer, and I know
something about DACs and ADCs. But, I've never designed a circuit with one and I'm not up-to-speed on the current market. (We do use a Burr-Brown ADC chip in one of our products, but it's not an audio or video product, and I didn't design it.)
These are ICs (chips). The chips have to be designed into an entire circuit. That overall design will have an impact on the quality of the "product"... In other words,
the soundcard with the "best" chip, may not have the best sound quality. For example, our product uses some "digital calibration", so we can correct minor errors and get accuracy that is actually
better than the raw chip-specs! Oh, the individual chips vary... The manufacturer's specs are "worst case", so some require more calibration/compensation than others.
You didn't give a Burr-Brown part number. If you know the particular chip, you can probably find the "datasheet" and dig-up and compare the
accuracy and
noise specs. (Here's the WM8785
datasheet.) You can compare the other specs too... But, I am assuming the "basic" specs are similar.... I assume they are both 24-bit chips, and I assume they can both go up to 196kHz or higher. (And, there will be a lot of information in the spec sheet that you don't understand, and much of it you don't need to understand unless you are designing a circuit.)
Burr Brown (now owned by Texas Instruments) has a good reputation and has been in this business for a long time... Maybe since before digital audio was mainstream. (I
know Burr-Brown made low noise op-amps before CD players existed, but I don't know when they started making ADCs & DACs.)
I don't know anything about Wolfson. But, that doesn't mean anything... Like I said, I'm not up-to-speed on this market/technology.