I had looked at the current more compensation circuit in a simulation and AFAIR the compensation part had the same effect as an addition 1st order filter stage. Same attenuation and same extra settling time. As digital inverters are relative cheap it could still be wort it, but the response of 1 st order filters is still not ideal and a proper 2nd order filter may be better performing.
The simple 2nd order Sallen-key filter can have the problem of direct feed through via the capacitor in the feedback, if the OP amps is not very fast. So ideally one would have a 3rd order filter with an extra passive stage in front.
I don't think the voltage compensation would be significant different. As a first crude guess mainly a shift in the cross over freqency and this way faster settling but likely more ripple to start with.