I skied on a river for 10 years, current was anywhere from 0.2 to 0.8 mph. Zero off wasn't created then, we adjusted our Perfectpass speed by adding wind. In terms of boat speed, this worked well.
As far as the skier goes, I found it to be like skiing wind, but with glass water. I personally find it easier to ski upwind, and also found it easier to ski up current. Against the current, generating the same lateral vector, which is what is required to reach the line of the turn balls before actually reaching the turn ball, will generate increased lateral velocity compared to with the current. This gets us to the width of the ball earlier, with more set up time for the turn, on the up current pass. Like skiing with wind, one does need to pull longer going up current than down. I found that time pulling and slack issues were similar to skiing in wind.
The other issue is the ideal speed for which the ski is designed. I've always used a 36 mph ski and skied at 34.2. Naturally, the ski performs ideally at a faster speed, relative to the water. So, on the upstream pass, I felt the ski to be more responsive. That said, the smoothest, easiest short line pass I ever completed on the river was a downstream 32 off pass. Can't really explain that.