I also own both. Model 1873's. I have no real preference between the two. Both are very well built, function reliably and are accurate. Still, I do tend to prefer the Uberti-made rifles over Winchester. But.....for very specific reasons.
As most active cowboy action competitors already know, to be competitive in the sport it is often necessary to modify these firearms to function fast and reliably, under tough competitive conditions. So that means swapping out various springs and other parts.
This is where Uberti rifles really shine. There are any number of top quality, aftermarket parts available, to achieve this goal. For example: reduced power springs, lighter cartridge carrier blocks, short stroke kits, and so on. So, it can be relatively easy to modify the stock rifles for top performance. It comes as no surprise then, that the vast majority of top cowboy action competitors run the Uberti brand, as their main match rifles.
Winchester-Miroku rifles on the other hand....since they are a relatively new kid on the block, lack that aftermarket support. So fall a bit behind, in that regard. If cowboy action shooting may be in your future, that might be something to consider, before making a purchase. Still, that's no reason to turn your nose up at one.
It bears mentioning that, this situation is slowly improving. As more aftermarket parts intended for competitive use are starting to appear. Also, if a person is even moderately mechanically inclined, the Miroku-made rifles can be modified to run nearly as fast as their Uberti counterparts, with a few simple mods.
Still......the Winchester-Miroku rifles, even in stock form, can perform very well in competition. As they are very smooth operating, have good triggers, and already come from the factory lightly short stroked. If you look up former World Champion: ' Deuce Stevens', you tube channel, among his various videos you will find a segment where he takes a stock Winchester 1873 from box to range, and demonstrates how capable one of these rifles can be, in actual competition. From my own experience, I can state that these rifles can and do hold their own in most competitive situations.
You cannot go wrong purchasing either brand. As mentioned though, a person's end purpose might influence choice.
Hope this helps
Al
ps: Maybe not part of this particular post, but, I also own a Pedersoli 1886 rifle, chambered in .45-70. Excellent build quality, inside and out. Have also had the opportunity to shoot a Winchester-Miroku 1894 rifle. This one, chambered in .38-55. Top quality, throughout.