Here in UK we don't have many 'Clinicians' of the type referred to in this thread, very few that would be classed as high profile/high exposure like you do in USA, we tend to have specialists who specialise in the various disciplines eg. Show jumping, eventing, dressage ect.
Very few that actually specialize in foundation and general behaviour problems.
If you can't do it yourself then you take your horse and have it broken/started/trained by someone recommended by friends or by reputation within the field of your chosen sport, then further down the line you would find a trainer and attend (usually private or small groups) lessons, (uk being so small you don't have to travel very far to find someone to teach you and any given discipline)
A lot of children are bought up going to pony club (you own and keep your own pony as opposed to riding schools where you hire ponies) and instructors are available in all discipline for a moderate cost, qualified riding instructors can be found every where!
But to my mind riding and keeping horses is not just about being able to ride well in the show ring or cross country but by being an allround horseman! We are good at getting good riders but not so good at being good horsemen! Sorry to be going on a bit
Monty Roberts was about the first Natural Horseman to come to UK in the 90's and for me was the first time I was exposed to new ideas and made me think outside the box of traditional British horsemanship.
Enter Natural Horsemanship! (40 years both professional and private horse ownership) but it was not until 2008 that I attended a Parelli celebration in UK that I had my mind blown away at the depth/feel/and understanding that could be achieved when NH methods were used with knowledge and love.
I have followed the Parelli program for the last 4 years and wished with all my heart that I had had exposure to NH all those years ago.
Since learning Parelli I have not closed my eyes to other NH clinicians and have sort them out when ever possible.
On TV I can now see many of the clinicians that you get in USA ; Chris Cox, Craig Cameron, Clinton Anderson, Buck Brennaman and many others. I have also watched live the last 'Road to the Horse' and I must say that I was disgusted at the way Clinton acted towards both his horse and to fellow contestants (yes I know he won it years ago) he was so direct line wanting to win he had no feel, timing or care for that horse he just wanted the job done, ok you might think he got the job done but at what cost to that horses future? I think he deserved to come last!!
I don't think of it as to whom I would chose to teach me it is more of who my horses would choose to teach them that counts!! I would safely leaving any of my seven horses (by the way none of them have behaviour or attitude problems) with; Pat Parelli, Buck Brennaman, Dave Stuart (who I have attended clinics here in UK with) and the late James Roberts who was UK's own Natural Horsemanship clinician and my mentor for the last 2.5 years. But never Clinton, he still has too big an ego for my liking, lets hope he matures and looks back and uses all he knows with more feel, timing and compassion for the horse, then I think I might look again at what he has to say.
So don't ask who you would like but who your horse would chose!!