I think the difference between the two movements effectively boils down to one being stabilised by external forces and the other not. (This is by no means an exacting analysis but may help explain why pull-ups and pull-downs are not the same beasties.)
Unless you are using body English (eg. for kipping pull-ups), a regular pull-up or chin-up will have your centre of gravity fall pretty much directly under the bar during the lift. When performing pull-downs this is not going to be the case the whole time. There's the seat position relative to the line of the cable and you also have a moment of force being applied onto your knees by the restraining pad away from the line of your centre of gravity. The ability to stabilise yourself during the movement (your iliacus, psoas and the muscles of you core are actively engaged) effectively helps you to learn the best way to pull the bar down, altering your back angle, shoulder rotation as required at the appropriate moment to complete the movement.
To a much lesser extent (and depending on the machine), there is always some inherent friction in a pulley system, making the eccentric slightly easier than the concentric.
The difference between the two isn't huge once you have learned to do both, but the fact remains that there is a difference; for me, as a pull-up or a chin is a more functional movement, I'd rather get good at those than any machine variants.
One plus to using a machine is that the load can be kept consistent (assuming you stick to the same machine); body weight fluctuates. So, unless you weigh yourself each time you do a chin or pull-up session, you aren't going to be able to make an exact comparison with a previous session. It's probably a good idea to make a weekly note of your bw on your w/o log so comparisons with earlier or later sessions are more meaningful.
As an aside: my teenage lad has never used a machine. When he first tried he couldn't manage a single strict pull-up. A year or so later, he's recently done 16 full-ROM reps and now has his sights on 20. In that time he has grown a lot too which makes the achievement even better. I'm going to get him to add some weight now.