I don't have any experience with a Rossi. But I've owned a few Chiappa's and Winchester 1892's. As well as some Henry's.
This is all subjective and based on my own experience, a limited sample size.
I had one Chiappa Alaskan, it had a lot of slop in the lever, it locked up, didn't feel tight though. The second one I had was much better. Still had some slop in the lever, the lock up was much better. Both had smooth actions, and nice triggers. I kept the better one, and sold the other. Mine has a 12" octagonal barrel with the chrome finish, and black rubberized stock, Skinner sights, pic rail, and it's in 357. I can hit a 8" gong at 100 yards with no issues.
I've also had a few Winchester 1892's, trappers, deluxe trappers, short carbines, etc in 357 as well. All of these were Japanese Miroku guns. These were by far much nicer, and had better quality. They all locked up tight, had no slop in the levers. The case hardened ones were gorgeous. I really didn't like the Buckhorn sights on them, but that's personal preference. They also have a safety. I think the browning 92 are the same as these, just no safety.
I've had a few Henry lever guns, but only have a long Rangers express now. It's in 223, and not a 1892 pattern, so not exactly apples to apples. And none of the Henry's I had were in 357 either.
The chiappa is nicer and more smooth, but the Henry locks up better and has less slop. The Winchester is nicer than both. Never had any issues with any of the rifles that weren't user induced.
I don't have any experience with the Rossi, so can't comment on them. If we get the nicer models with the octagonal barrels here like they do stateside, I wouldn't hesitate to grab one.