I confess that this is mostly above my paygrade. I thought White's was stitched-down as well... But I am pretty sure that Viberg's can be resoled without replacing the upper; lots of folks talk about getting them done...
In any case, I certainly wouldn't question the toughness or durability of White's, though aesthetically there does seem to be some quality control issues on occasion. Not a big deal for work boots of course, where looks are secondary to functionality.
Like I said, I'm just giving my opinion of liking the White's welt better. Both types can be resoled several times, but the portion of the welt you see sewn through on White's is a strip of leather sewn to the rest of the leather upper. The strip can be replaced once it has too many holes in it That is the gist of a "Goodyear welt". On the Vibergs, the portion of the welt you see sewn to the sole is just the upper leather turned outwards, pressed flat, and sewn to the sole.
The welts in both cases are sewn and glued, and really are about the same waterproofness. The issue that bothers me is where the welt ends by the arch. The White's Goodyear welt has the strip sewn down, and the rest of the upper forms a booty that is folded in under your foot. On the Viberg, the upper has a notch cut in it to allow it to fold under at the end of the welt seam. If care isn't taken during assembly there can be an actual gap at this point, and that would be the area most likely to allow water in.
I'm insane when it comes to this stuff, so who knows if it has any affect in the real world beyond my delusions. White's, Viberg, and Wesco all have excellent reputations.