I have a Winchester 94 .44 magnum from the first generation built and they run short cartridges just fine. Back in the day the most common .44 magnum cartridges used semi wadcutter bullets. The radical stepped design of that bullet does tend to interfere with the action. However, when running ammo with common rounder profile bullets, the action can be worked without any problems.
I love my Winchester, it's extremely light and shoots like a dream but unloading it is a PITA. That's why I love my Henry Big Boy .45 Colt, yes it's heavier but it soaks up recoil like a dream making fast followups much easier and unloading a magazine full of ammo is insanely easy. The Winchester requires cranking the lever for every round left and then gathering up the bullets that go everywhere with that design. Back in the day when these guns were used for combat, loading on the fly was absolutely necessary and magazines were usually kept topped off. Today, neither is needed. There's no life or death need to fire 10-14 rounds and keep topping off the mag. Even when plinking very few folks will burn through that much .44 magnum or .45 Colt at a time. Since we don't generally keep our lever guns full at all times, especially when they have to be transported, having an easy, fast way to unload your mag into a nice, easily managed pile is a blessing. I just open my Henry and pour the ammo into a hat. With my Winchester it takes significantly longer, far messier and the cartridges tend to get dinged up from hitting wherever they hit.
Not to mention the Henry rifles are insanely accurate, which definitely doesn't hurt.
Don't write off either one.