My bunnies must be in the hay minority, since they usually go for the stemmy bits first, so they've always enjoyed the coarser first cut than the soft second cut.
So I would say both would work, but it's usually just the individual preference of the bunny.
Someone might know this, but for the nutritional value, isn't the higher the cut, the more nutrients in it? But with the lower the cut, more fiberous? Hmm.. I'll have to look that up.