I've owned two .44 magnum lever guns. My current, and best so far, has been a Henry Big Boy (a bit on the heavy side, though).
In any case, it comes down to range. The effective range of the .44 is about 100 yards, max range might be 125 or 150 yards. If you're shooting past those distances, then the .30-30 will have more range.
Otherwise, the .44 magnum has some impressive ballistics from a rifle inside of 100 yards and for a short range rifle it's my choice. Not to mention .44 specials can be fired from the same rifle for reduced recoil with impressive ballistics. Even though you may never own a revolver, it's also nice to know that you could purchase a handgun in the same caliber as your carbine.
For longer ranges I have a .308, which is cheaper to shoot and reload (cheap military brass), has more factory loadings available and is more powerful than the .30-30. In guns that I shoot, I'm also not limited to special polymer tipped rounds, round nose bullets, or loading singularly to prevent detonation unlike a .30-30 lever gun.