Two things come to mind when I follow your link. First is that the stocks on that gun *MAY* not be original and I simply have to use the term *MAY* because the 581/681 is scarce enough that I simply don't see them. I had a friend back in the early 90's who brought one along on a range day (it belonged to his brother) and it was the only time I've ever handled a 581 and I bet I have seen maybe 2 or 3 other since that time.
Of course, I say this as a guy who has not specifically been chasing them, I may have overlooked some without noticing... but it's safe to say that since that time, I've seen many dozens of 586's and a
gujillion 686 revolvers. The wood stocks shown in the pic with that 581 are the older style Magna and the 586/686 of that vintage
all came with the Goncalo Alves stock (Goncalo Alves Target maybe was the name?)
If I had to guess, I might suggest that the pictured revolver was some manner of a service issue or contract fulfillment for some agency? But I really don't know. Stocks of this era are not marked or numbered to the gun iteself, but I have two S&W revolvers from the 80's that I got new and those actually have a production date stamped in ink inside them.
The other point I want to make is that a 581 no-dash is subject to a still active and honored Smith & Wesson recall. This is not some catastrophic issue, it's a replacement of the bushing around the firing pin hole in the breech face and all evidence has been that S&W is still happy to handle this quick and easy work if/when you have the gun in your hands and you contact them. Behind the crane/yoke on the frame will be an "M" stamp if the revolver has already had this recall performed, and no stamp if it has not.
My opinion? May not translate at all to your needs -- I am a shooter and I absolutely
love to shoot and own a variety of guns. As such, I will nearly always choose the handgun with some visible exterior wear and a SOLIDLY lower price than I would for a (seemingly!) "better" finish priced higher. That is simply how I enjoy my hobby, so if you're looking for opinions on which way to go, I like the first one better at $450... but in defense of the second one, if the seller is a "bona-fide" gun dealer of some manner, it should bring a little piece of mind with regards to packaging securely, shipping to FFL, etc etc.
Even still, I'd choose the first one. But definitely update this thread, I love a happy ending.