Howdy
I have a couple of Uberti rifles, and I like them just fine.
Model 1873, chambered for 44-40.
1860 Henry, chambered for 44-40.
I have a few old Winchesters too.
Model 1873, chambered for 38-40.
Model 1892 Rifle and Saddle Ring Carbine, both chambered for 44-40.
Model 1892, chambered for 32-20.
No, I don't have any of the modern Winchesters made by Miroku, but everything I have read about them is they are top quality.
I also agree that for the OP's purposes, the availability of after market parts should not be a concern, he is not interested in completing with his rifle.
I have not checked recently which one costs more, the Uberti or the Winchester/Miroku. So I can not be of assistance there. Let your pocketbook be your guide. Yes, ALL Uberti firearms have soft screws. That's just how they make them. And the first time you go to take an Uberti apart you better have a good set of gunsmith style hollow ground screwdrivers, or you will probably bugger up the slots on the soft screw heads. I have no experience with Miroku screws. Yes, you can get hardened screws from VTI Gunparts.
You may have noticed I have a preference for 44-40, as well as 38-40 and 32-20. Those were the cartridges the original Winchesters were chambered for. 357 Magnum had not been invented yet, and rifles were never chambered for 45 Colt in the 19th Century. That is a whole nother story.
But having loaded these cartridges for many years, I will say that while they are not 'difficult' to load, they do require a bit more care than say a 45 Colt or a 38 Special. That is because the brass at the neck is much thinner with the old WCF cartridges than the venerable 45 Colt or even 38 Special (or 357 Mag). If your dies are not set correctly, or if you are rushing, it is easy to crumple the neck of a 44-40 or 38-40. 45 Colt and 38 Special are much more forgiving in that sense.
So if the OP wants a '73 chambered for 357 Mag/38 Sp, I say go for it. By the way, the Uberti short rifle chambered for 357 Mag is the rifle most of the serious competitors in CAS choose. 38 Special and 357 Mag ammo are available everywhere. 44-40 and 38-40 are not.
A word about the strength of a toggle link rifle and 'hot' cartridges such as 357 Magnum: All firearms produced in Italy are proofed in government run proof houses. European proof loads are slightly hotter than those used in the US. So leaving the factory, any Italian rifle has been proofed with proof loads. I have no idea about Japanese rifles, but I'll bet they are proofed too.
I will say I once saw an Uberti '73 chambered for 357 Mag with a cracked frame. It was on sale used and the crack was barely noticeable, but it was there. No idea how the frame got cracked, no idea what the loads fired in it were. I'm sure a modest diet of 357 Mag will not hurt a '73 made with modern steel. You might not want to shoot much anyway, the report from a short barreled rifle will be very loud.
Both the Mirouku and the Uberti 357 Magnum lever guns can also be fired with 38 Special ammunition. Sometimes there is a problem if the Over All Length of a 38 Special cartridge is not quite long enough, but most factory ammo should cycle fine.
One more thing. Both the Miroku and the Uberti '73 will come with a lever safety. This is not a modern lawyer dictated device, it was first incorporated in the Winchester Model 1873 around 1879. With the toggle link rifles, if the links are not lined up straight, in other words if the lever is not closed all the way, and the trigger gets brushed as the lever is closing, recoil will drive the bolt back, folding the links. The shooter's hand will smart as the lever is yanked forwards. I saw one lever that was completely broken off when this occurred. In past years, a lot of guys were removing the lever safety, because its spring is strong and slows down fast shooters when they close the lever. DO NOT REMOVE THE LEVER SAFETY. After market springs are available now so the stiff factory spring can be replaced and it does not require an iron grip to close the lever.
In this photo of my Uberti '73, the small part poking down from the frame is the lever safety. You can see the other half of it directly behind the trigger, blocking the trigger from being pulled. As the lever closes all the way, it pushes up the rear part of the safety, which also pushes up the part blocking the trigger.
Look what I just found. Here is a photo of my 38-40 '73 which was made in 1887. The arrows are pointing to the lever lock. The side plate has been removed and the links are completely folded because the lever is all the way forward.
In this photo, the lever is closed. The lever safey has withdrawn all the way up into the frame so the trigger can be pulled. Over on the right the bent piece of steel is the main spring (hammer spring). Just under the main spring is the smaller spring for the lever safety.