The probability rescaling has involved an exponentiation step, such that the scores are all positive and may be interpreted in a ratio sense (e.g., a 6 is twice as important as a 3). The zero-anchored interval scale just involves a shifting of all the raw logit-scaled utilities such that the anchor is the zero point. These utilities may not be interpreted in a ratio sense.
Depending on whether the anchor is, the probability rescaled scores can tend to squish the least desirable items all pretty close to zero, so if you are interested in discrimination among least-preferred items, this might not be helpful. But, the ratio interpretation is nice.