The advantage to the Clinton Anderson rope halters, in my opinion is twofold:
First, the additional knots do provide a bit more pressure to get and keep your horse's attention.
Second, they are made from much stiffer rope which also provides more feedback and pressure for the horse.
That being said - don't pay the prices Clinton Anderson asks for them. You can find rope halters that are identical to the CA brand - same knots and literally the same rope on ebay
for less than half of what CA and other big name clinicians charge. I have two of them and really like them.
They are also quite a bit more durable than the tractor-store variety.