I don't think pulling wire is that likely, at least probably not with recent construction in a place with code enforcement. Standard here would be a 120v 20 amp circuit on 12 gauge romex... I'm not an electrical engineer, but shouldn't that be sufficient for nearly 2000 watts constant load? I've done a little bit of homeowner construction to code, and they make you run a separate circuit for just about damn near everything these days, except lights... I guess the concern would be if you've got an old 15 amp circuit on skinny little wire or hooked up to your air conditioner....
Depends where you are and how old your house is. Kitchen ones are often 20A, though in my house (early 70s vintage) they're all 15A.
Regardless, you likely will be pulling wire no matter what kind of branch wiring you have, since even if you have 20A branches drawing 1600W/1800W on it would basically make it useless for every other outlet on it. There probably won't be many Sierras on residential branch circuits, but having your miner down for a weekend because you're out of town and your wife turned on the TV seems like a recipe for marital strife.
BTW-There's almost no difference in this mostly pointless discussion between the two 850Ws or the one 1600W supply, since anyone plugging these into residential circuits would almost certainly try a few times to plug both supplies into the same branch circuit.