Each has their advantages. Over the years Marlins have been consistently very good. Winchesters quality has been all over the place, but if you have a good one, they are every bit the equal of the Marlin. Generally the Winchesters tend to be a little lighter, the Marlins have the advantage of side ejection if you want to mount a scope. If not, that does not matter.
If I had a good Winchester, I wouldn't let it go to buy a Marlin. If you just want to buy a 2nd rifle, I think the odds of getting a good one are a little better going with the Marlin. Especially in the used market.
This is my favorite and the best of both designs. A 1973 Marlin when they made them with a lot less wood in the forend and a lot less weight.