Every Marlin I've handled has had a smoother lever action than every Henry I've handled. But for whatever reason, Henrys just look cheap to me.
Like I said, I own 1894s in 3 different calibers. I also own a near-new condition Marlin 336 in .30-30, made in 1969. The round bolt action of the 336 is smoother than all of the 1894s.
The Henry action, incidentally, is simply a reverse-engineered copy of the Marlin 336 round bolt action.
Internally it's virtually identical.
The .30-30 and .45-70 models even use the same extractor design which is formed from a hardened steel stamping. The Big Boy retains the round bolt action but uses a spring and claw extractor.
Most people that own them comment that the action is very smooth. And you get an octagon barrel and high quality Marbles sights on the Henry brass Big Boys. Henry rifles all have decent triggers as well, where Marlins often have heavy ones.
I was very impressed with all of the Henry Big Boys and .30-30s and .45-70s that I have examined. They all had beautiful walnut, glowing brass, and superior smooth blued steel finishes, with first class workmanship.
And, the use of Marbles sights was also higher quality. The standard Marlin front sight has been a brass casting painted black for many years. Not great.
You only get the Marbles sights and an octagon barrel on the Cowboy models, and you pay a considerable premium price for these features.
The only things that I disliked, other than the weight of the brass Big Boy and the lack of a loading gate, was the look of the trigger, which seemed a little odd compared to the Marlin ones.
In the end, I would encourage anyone wanting to purchase either rifle to examine each of them in person before you buy. It's the only way to know for sure which one to buy.