I have to say that when I first used a carrot stick I did not find it an easy tool. It is something I had to learn to use properly. In fact in the program they suggest a few exercises to get handy with the stick and string which only take a few minutes but do make a big difference. It is such a versatile tool that does take a while to get a feel for how to use it in different situations.
I know that you could switch tools according to the situation and use a lunge whip for circling, a stiffer stick close in etc. But with a little practise the carrot stick can passable do all these things and I don't have to stop the exercise to get the tool I need now and miss the moment I need it in.
As for making a noise that's easy. Just hit the ground behind the horse with the string, that makes a big noise !
If I am working close in with a horse I tend to not use the stick and string, but the stick with a bag on the end. An even better tool when close in is a horsemanship flag Horseman's Flag
. Just wish I could work out how to make one cheaper. And people say Parelli equipment is expensive
. The disadvantage of this is that I have switched tools as noted above.
Again when close to the horse, if trying to get it to yield to steady pressure then I find that the stiffness of the stick is a great asset. Horse can lean on the pressure from the stick as much as they like and it will barely bend which teaches them that pushing into pressure does not work. If it were to give then they would learn pushing does work. I know you can use your fingers for this, but when working with a horse I don't know I prefer to be 4 feet away to start with and the stick allows this. Maybe I am just a coward.
I often turn the stick around if I need to really get the horse out of my space as the handle has more weight to it. I can then tap them with the handle end if needed to get them to back out of my space. That is something you really can't do effectively with a whip.
If you want to work a long way from the horse I sometimes add an extra string to the end of the first string to almost double the reach. The length of the carrot stick (4 feet) the string (6 feet) and your arm (2 feet) is designed to make the combination the right length when using a 12 foot rope. Using a longer rope you may need more length, but then you shouldn't be on a 22 foot rope until the horse is responding pretty well to the cues on the 12 foot rope.
In summary I would say that there are tools that will do specific jobs better. The lunge whip has been developed over years to be good for circling a horse after all. But like a Swizz Army Knife the carrot stick makes an adequate job of doing many things well enough without having to switch tools mid flow. With this in mind it is not really fair to compare the carrot stick with specific tools for a specific job. The question to ask is "is the carrot stick good enough for the task ?", not "is it perfect for the task ?".
As to whether the CA or Parelli stick is better I have no idea, but they look the same to me. I would be careful about buying cheaper imitations though, they tend to not be stiff enough.