The segmented ones are:
a) usually cheaper
b) have a little more "heft" to them, and hold their elliptical shape a little better while spinning
c) won't turn quite as fast as a good leather rope, if you want to go fast (but a true speed rope with a tapered center section will go even faster than most leather ropes)
d) aren't as good for "trick" work (crossing arms, etc.) as a leather rope.
For most straight jumping for warmup and endurance training, I think it's a toss-up.