I own the BDP-83 (standard model) and OPPO's 980H. The BDP has marginally better sound quality on CDs, noticeably better on SACD, and (to me at least) sounds worse on DVD-As (of which I have only a few). The differences are not huge. I wouldn't want to bet my house on spotting them in a blind test between the two players.
My dedicated CD player for the past 12 years has been an Audio Research CD1. I had hoped to sell it once the BDP arrived, but the ARC is way better for redbook CDs. As Cmalak said, there's an edginess and grain to the OPPO, not overwhelming, but certainly there - this disappears with the ARC.
A while ago I was actually comparing the ARC and BDP playing a Haydn string quartet at reasonably high volume - my wife was in the adjoining room and when she walked through even she noticed the difference immediately. The OPPO does add a sense of strain and sharpness to the highs. With a string quartet, or most classical music for that matter, it makes things tiring/irritating.
Another rough comparison - an SACD through the BDP sounds close to a CD played through the ARC CD1.
Rest of system = ARC SP9MkIII; Wyred4Sound ST1000; Usher Be718s; REL Storm III sub.