Older 39A's, as salvo said, didn't have the rebounding hammer and crossbolt safety.
The 39AS has them, though, right? So it's mechanically no different, AFAIK.
I have a pre-safety 39 and the current model.
The mechanical differences do not influence which one I want to shoot.
The difference between the ones I have is that one's essentially identical a lot of 1897s I've seen: straight grip, skinny foreend, 20" tapered octagon barrel -- looks like the current Cowboy centerfire guns Marlin sells. The other is a current 39A with the pistol grip stock, curved lever and 24" heavy round barrel.
Frankly, I prefer the modern one usually, since it's a full-size, full-weight gun and is easier to shoot at 100 yards offhand. I plink at a buffalo gong target a friend traded me for a couple old reloaders when I moved.
The safety can be a problem if you forget to check it when using the gun. However, you don't have to use it; you can leave the hammer down and cock it when you want to shoot. The safety allows you to lower the hammer in complete confidence that you won't set off a round.
So, as much as some people hate the safety, it has its upsides -- and it can be locked if you really don't like it.