I would have to rate the Browning and Winchester as qualitatively superior to the Marlin. All three are MUCH better than the Henry. I do not like the Ruger 96/22 lever gun... basically a 10/22 with a geared bolt and lever. I have owned and/or extensively shot all of these rifles.
The Browning is a little trimmer and lighter than the Winchester, and of course has that short lever stroke. The disadvantage of the short stroke is that it takes more effort to get everything moving... just something you have to get used to. The Browning is the prettiest of the lot.
The Winchester has a smooth action and in my opinion just has the nicest 'feel' of any rimfire lever action. I really like the weight and balance also... not too light and not too heavy.
The Marlin is a solidly built gun (I like the pre-button safety versions) but the design of the action leads to more inherent friction. I prefer the 39M version with the straight stock and shorter barrel.
The Henry? It is an adequate shooter, with a very smooth action which is a result of the material used. I do not like the plastic and pot metal accoutrements. For the price I'd rather have a 10/22 or a CZ 452 Trainer... but I have never let price influence me when buying a gun. I buy quality and if you have all four guns in the same shop at the same time (as I have had) then it's easy to separate the winners from the also-rans.
My personal favorite is the Winchester 9422 20" version... holds a lot of shells, shoots everything accurately and reliably, holds steady, and is reliable and rugged. My personal rifle is hard chromed and looks really sweet... and it is the gun I grab when I'm heading out to the boonies and want to play.