SL is correct about Wilson and Clerke barrels being the manufacturers forthe majority ofWhite rifles, but some early ones were Green River Rifle Works, some Douglas, some ?, then came the Wilsons, then the Clerkes, and just for a very few of the most recently made specimens - Criterion (make Weatherby barrels).
The barrels from the different vendors areslightly different so far as crowns, number of lands/grooves, and even barrel tolerance values. There are even a few rare piecesthat have 12-groove barrels. My preference is the Clerkes - the crown ismore a funnel shape and not so picky about initial alignmentas are the Wilsons withtheir recessed target crown(IMHO). The Ultra Mags all have Clerke barrels so far as I know.
Wilson left, Clerke right
The Wilsons have the advantage if comparing barrel to barrel dimensional consistency - but no apparent advantage accuracy-wise.