It depends on why I want it. Rossi don't usually have the same degree of fit and finish, but can be polished up to be nice rifles. What they can not be is modified for side eject. If you want to make it into any style of tactical bolt action (other than perhaps mounting a red dot on the rear sight dovetail), you will probably find frustration. If you just want to play cowboy-they can be excellent rifles. I think the Rossi ones were probably all decent looking (better than the older Puma branded ones). I have 2 Rossi - one back from the Puma days, but were built to a much better spec (it is beautiful, and after a bit of work a joy to shoot. The other is a Rossie Mare's Lag - Ok out of the box, but I have modified it a bit to make it more palatable as well). Miroku Winchester versions are probably the nicest-but those probably cost a mint right now. I have sinned - I have 2 that I have not even shot (my older brother decided to get out of gun collecting, and I was all but given his collection since his kids were utterly not interested). The Miroku were always out of my price range at the time.
I have a bias against Henry's. It has no rational basis. I don't think Henry had any 38's in production when I started my lever collection - perhaps that is the basis of it.
Marlins don't look as nice to me due to the square bolt - but I love shooting them so have a few. I have a JB's (prettiest), Marlin (ok, worked on a LOT, but started life with me as a busted up truck gun that I did not even shoot till it got rebuilt-which cost more than the rifle), and Remlins - they have all worked great (ymmv), and a slicked up Marlin will be better than a slicked up Rossi. There is a reason they were the most common rifle used in CASS. They also had a reputation of being more reliable than the Rossi and Uberti's.
There is also the Uberti's - the 1876 can be made slicker than anything else out there - but they are heavier. fwiw-my brother kept his Uberti and Army San Marcos (1892).
Don't do an 1894 unless you have a valid reason to do it. It is compact, it looks good (ok, they made some that looked good and some that looked like shit), but the action is rediculus. If you do need an 1894, just get it in 30-30. I think I have 2 that look like shit - but they were my wife's uncles guns, so have grandfathered safe space. Winchester truly turned out some ugly guns, but they were chasing the dollar and that meant they made some that cut every penny possible.
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So, to answer your question, what would I do... If I just wanted a caliber - I would probably get what is available. But preference tends to be Marlin. Correct answer is get both. Get what you can now, and upgrade it later if you want to. Looked at both Rossi and Henry web site - Just not feeling the love there personally. None of the Rossi models look anywhere close to as nice as the one I already have.