Talk about complicating your life
Over sampling filter is a must for removing digitalization effects, you just can't go by without doing it. Having said that, the vendor usually offers the standard band pass filter response and the slow-roll off one. It's up to the designer to program it to be turned on or off (just a one bit toggle on the control line).
Most of what everyone has said partially explains the effect of either not using it or switching between the two modes. I wish ESS tech would publish their roll-off curves the way Wolfson does but unfortunately they don't. Assuming they use a similar technique than Wolfson, the band pass attack in both roll-offs are about the same, it's how wide each allow frequencies to be filtered and at what dB level signal they do. The big difference between the two is about 1/10 of the bottom and top band pass frequencies which comes to about 2 hz at the bottom and roughly 2 kHz at the top. As most instruments and female voices have a top range that's way below the top cut-off frequency, the harmonics are what you'll capture and hear, not the top band which is too high for most listeners. What most listeners described could either be pleasing to the ears of clinical to others but what's nice is you got a choice. Wolfson as such uses the standard filter action which is the sharp one as the default. ESS does not mention which one but I would suspect it's the sharp too.