Have hunted with Ruger #1s for years and like them very well. Most don't really need any foolin' with unless you think deer have gotten smaller over the years....Most hunters really need to have the first two shots hit within about 2 1/2" inches of one another every time at 100 yds. Varmint hunters need better, but most don't use #1s, and most #1Vs WILL do better. Vertical stringing, the most common #1 bugaboo is, IMO, born of the "five shots under 1" syndrome." Nothing to do with most hunters REAL need; mostly just for gun writers to have something to write about. I've had a #1A .243, a #1S .45-70, a #1RSI 7x57, an RSI .243, and some custom jobs, not to mention various #3s. The stock #1s were all "deer accurate" right out of the box, including the one with the much-maligned Wilson barrel. Still have the RSIs; they still shoot. (It is possible that I've been lucky; Ruger does sometimes make real "lemons"....).
I have no experience with the Browning. Does its action function the same as the original 1885 (hammer stays cocked when you close the block?). Or is it like the coiled mainspring "later" 1885 that has a fly that drops the hammer to half-cock when the lever is closed?
If it is like the later 1885, I would choose the Ruger for hunting purposes because it is faster to reload and fire the second shot. You don't really need that second shot very often, but when you need it you REALLY need it RIGHT NOW!
For that reason, I hope Ruger never gets the "lawyerly" notion to replace the non-automatic safety on the #1 with an automatic one.
IMO Johnnie Browning's original creation as re-designed by Winchester, the "flat-spring" 1885, is a better hunting rifle than either the #1 or the Browning, if in fact the Browning needs to be re-cocked before the second shot. Too bad they are so scarce and expensive!