As between those two watches, I'd certainly choose the handwound. But in the great wide world of $8-10k watches, I'd almost certainly make a different choice. The Portuguese (and from here on I refer to the handwound only) is a beautiful watch possessed of elegant design features. My issue is with its dimensions. Others will no doubt quickly enter a galssy-eyed trance and rhapsodize about the historical entecedents which inform the present day rendition. I'll happily leave that to them and simply make some comments about the watch itself, since it is the watch you would be purchasing.
44mm is big for a dress watch, IMO. Really big. In a sports chroograph or a dive watch, a case that big is more than okay. But for me, a dress watch of those dimensions simply doesn't make sense. The substantial case diameter is visually exacerbated in the Portuguese by three factors: 1) short lugs, 2) thin case and 3) thin bezel. The end result is an "all dial" watch that looks even larger than its immodest dimensions suggest. It takes a hefty wrist indeed to wear the watch and not have it appear that the watch is wearing you. A pancake on a strap is a look that will work for some, but not for others.
So if the goal is to get a Portuguese, the hand-wound is definitely the one to get, IMO. But if the goal is to get an elegant dress watch in that price range, there are many more appealing options out there. And yes, the foregoing reflects my personal and entirely subjective aesthetic preferences. Though I'm sure that will not deter the usual suspects from telling me that I am "wrong".