Interesting responses, so far.
The Browning, and then later the Winchester 1886's of the modern era are all manufactured in Japan under the auspices of Miroku. The Japanese redesigned the original weapons to work on the metric system, additionally, they changed some, tho not all of the internal parts. It is for this reason that I believe the Browning/USRAC/WRA Miroku guns to be in effect different rifles from those made by skilled American gunsmiths so many decades gone.
This is not to disparage the new weapons, in fact I think they are quite nice, yet they tend to have slightly different enough dimensions and handling/action characteristics to in my mind at least, be qualified as replicas rather than continuation of the storied Winchester 1886.
Browning versions, which maintain the closest to original lock work, also tend to be heaviest of the replica guns. Part of this is due to the configurations chosen.
Some mention was made of the Browning carbine, and its inability-or ability-to shoot. Having some experience with the Winchester 1886 carbine, I can state that the gun must be held firmly, and high enough on the shoulder to gain the sights without undue craning of the neck in order to repeat its shots in a close cluster. By the way, the Winchester weighs in at least a couple pounds lighter than the hulking Browning.
Secondly, even a N.I.B. gun should be checked for correct torque on all screws. Any looseness in the tang-even slightly perceptible motion will almost always result in vertical stringing. It also never hurts to clean the barrel, as all matter of barely visible nasties can lurk in there, even if she was a safe queen.
In terms of which gun is better, the Marlin or the Winchester, I think a lot of it has to do with preference. The real Winchester 1886's are now going on 7 decades old-and beyond. They are quickly disappearing from the realm of practical weapons, into the vaults of history.
A more valid comparison might be between the new WRA 1886 extra light and the original 1895 Marlin. Both feature 22" bbl.s, tip the scales at a bit over 7 lbs., and can operate at roughly equal cartridge pressures.
In terms of features, such as sling swivels, checkering-the Marlin wins. In terms of Handling, I personally believe the extra light with its straight stock is faster to the shoulder, esp. since it does not have a rubber butt to catch on your clothes.
Personally, I continue to be disappointed by Marlin's insistence on Popeye sized forearms, but then, most Miroku barrels do not have throats, which can limit the use of some bullets.
If I wanted the best value for my money, I believe it is the Marlin, however, if I wanted the fastest and best handling-it'd be the Winchester.