I haven't used Parelli or Clinton Anderson anything because I haven't done any real training, but I do know that the halters are all the same. You can get a rope halter at a tack shop for probably less than $10 that is the same. They are essentially the same design, but they all serve the same purpose and get the job done.
Actually there IS a difference in rope halters; halters from fleet supply stores, and the like often are alot 'softer' with less 'feel' to them, so it takes alot more work to get the horse to feel what you are trying to get across.
I didn't really believe that either, until I started purchasing rope halters from people who had made them out of higher quality ropes...my husband also purchased a CA halter and lead for me last fall, and all I literally have to do is twitch my hand a bit, and the horse feels it, and starts looking for what I am asking for; backing, foward, etc. The difference in higher quality halters/leads for ground work training is definite...in my book anyway, from personal experience.
OP, as far as the differences, and which you should stick with in regard to trainers; over the years, I have acquired alot of my horse training 'ideas' and techniques from personal experience, and LOTS of different trainers, not just one. If Parelli is working for your horse, then go with it...if you are finding you need a little more "oomph" to your training, look at someone else's methods and see what you take from that. About the only thing about Parelli that I can deduce that I don't really agree with, is the humanization he puts into his program (the whole RBI, LBI, etc) A horse is a horse...they are not human; some horses are smarter, dumber, less respectful, more respectful, or more stubborn than others, period. Don't put your horse's attitude and behaviors in regards to "work ethic" into a box...If you want him to move his feet, then get him to move his feet...don't let his 'brain type' interfere with gaining his respect; you determine how fast, and how long he moves his feet, not the horse...period, end of story.