Both the 1866 and 1873 rifles were among the first repeating rifles that were successful. They were chambered for cartridges loaded with black powder, which developed very modest pressures. These pressures were easily handled by the toggle-link locking system. While, to my knowledge, the Winchester 1866 and 1873 were not originally chambered for .38 Special, this caliber also develops pressures easily handled by the action of either rifle.
If I owned either rifle chambered for .357 Magnum, I would probably confine most of my shooting to .38 Special ammo, and use the .357 Magnum only for defense or (should it be necessary) hunting. I do not believe the toggle-link locking system will withstand the continual stress from the .357 Magnum, a round developing 75 to 100% more pressure than most of the .38 Special rounds you will find.
While I enjoyed shooting the 1866 and 1873 rifles that I have shot, I found their operation to be "clunky", when operating the lever, especially if I did so with any speed. This is an inherent trait of the locking action, and I am in no place to criticize the designers. While I find the "clunkiness" tolerable, it is still a thing to be overcome, rather than enjoyed, when shooting
I know of the "mystique" associated with the early Winchester lever-action rifles, and I agree that they are difficult to resist, when they can be found for sale. I would not be giving you the full truth, however, if I did not suggest that you also look at the Winchester 1892 replicas, made by Rossi. This is a much stronger, inherently smoother action, which is capable of tolerating pressures well in excess of what the .357 Magnum cartridge develops. One of these will shoot well, after a lifetime of shooting nothing but .357 Magnum ammunition. You may also find it more pleasing to the eye, than the two rifles you contemplate.
The .38 Special, by modern standards, IS often considered a bit "wimpy" as defensive calibers go. I think this reputation grew largely from the round's poor performance when fired from 2" and 4" barrels. As barrel lengths increase, so does performance, generally. Thus, a properly loaded .38 Special round fired from a carbine-length barrel is not the "wimpy" round associated with what gets launched from 2" or 4" revolver barrels.
I try to avoid the use of black-powder in my firearms, because it is dirty, corrosive, and very difficult to completely remove from the internal workings of my firearms. I DO clean my firearms conscientiously and completely. I nonetheless always assume that I've missed SOME spot somewhere, which I will find and get clean the next time. With black power, a spot missed means immediate corrosion, right there, and will continue until I find and clean it. By that time, the damage is done.
i advise shooting black powder in the firearms of someone else, who is willing to tolerate the extra trouble of using it, and fully knows how to clean it away. Use modern stuff in yours.
I think I am correct in assuming that your country (Sweden?) allows its citizens to load/reload their own ammunition. If this is so, I suggest that you investigate this activity, as it will allow you to shoot for less expense, and will enable you to make ammunition which works particularly well in your firearm.
If questions remain that I have not answered, please feel free to remind me. I will make every effort to answer them.
Also, your command of English is excellent. You are to be commended!