the position that Lange is better finished than Patek (at this price point) is based on a number of factors but one such example is Philippe Dufour asserting Lange was the best finished production watches (or some such).
I also personally see the anglage more uniformly applied.
Sub 300K USD pieces, I see Patek as more than sufficient for its general pedigree and prestige - but you wouldn't buy based on the finishing as the primary decision driver.