Before I bought mine I read a bunch of threads and the concensus was that they were very accurate. Can't say from experience all that much, my one and only 1885 is a Winchester/Miroku in .38-55 but it does very well with .375 jacketed bullets since it has a groove diameter of .3751". Best group so far is three shots into .243" but that's a fluke, most groups are a bit larger than that.
But I haven't worked with jacketed much at all since this is for cast bullet shooting but so far it's doing okay, putting 5 shot groups of several loads into 2" (with my usual flyer). Most of those with both store bought and my own cast bullets put 4 shots into about 1.25 to 1.5" and then a 5th opens them up to 2".
Still working on getting those dialed in...
Not wanting to turn this into a Ruger vs. Winchester 1885 argument but I'd always bought Ruger No. 1's and never even looked at the 1885 as a viable alternative. However after owning one and noting the quality of finish, polish, wood, trigger pull, etc. plus accuracy right out of the box, these days I'd choose an 1885 - especially since both sell at pretty much the same price point. I keep looking on gunbroker for another one, I see this year they're making them in 30-06.