Yes, you would lose the use of the Burr Brown by using a digital out. My suggestion for you would be to hook up both (digital and analogue) to your receiver/ amplifier. Use two separate inputs, and A/B them. Some receiver's have very good digital to analogue sections that may out perform the disc player.
When you A/B them, make sure to use an spl meter and calibrate the output levels to the same level in db. Many people mistake an increase in volume for an increase in sound quality. My guess, would be that once the levels are calibrated, their will not be a huge difference. If there is a difference, it will probably be rather subtle.