It really depends on the horses you're feeding. Generally second cut has a higher protein content and is much finer, softer hay, quite lovely to handle in fact compared to first cut; good for old horses who have trouble with coarser feed and need more protein, or pregnant/stressed animals for eg.
Good first cut hay should be absolutely fine for most horses doing moderate amounts of work, with good teeth and in good health. Second cut usually goes for a higher price, too.
Oh, also some horses don't even care for second cut, and some think it's a grand treat. It all depends.
don't worry, spiders, I keep house casually.
~ Kobayashi Issa
(1763 - 1827)