Lacy All Over has perhaps my favourite white bloom of the whites that I grow, though for me, the branching/bud count has never been anywhere near the registered stats. (I'm northern though.) I love that the edge isn't so yellow most of the time.
Fringy, although I don't think of it as a white daylily (maybe because the yellow edge is so strong?), does much better for me up north in terms of branching, vigor, etc. The blooms are still lovely, but I feel like I grow it for the edge/fringe/teeth, plant habit, and warm (though soft) colours more than for a white look.
Arctic Lace has been very pretty and has done well for me too.
My White Mountain clump has always made me happy. It has lower bud count and branching for me, but it's in a spot that gets a fair bit of shade compared to the rest, so that may be why.
Overall, I've had excellent branching at times on Arctic Lace and Fringy. Fringy has the best vigor and plant habit for me overall--nice juicy scapes. There's something special about the blooms on Lacy All Over and the way the edge flicks back and forth in places (though it has boring days too). However, my White Mountain clump has given a clean white, fresh look some days that has never been beaten by the others here.
