Horse training vs dog training?

So I'm stuck inside on a cold snowy day. As I'm flipping through the channels on the boob tube, I found a show on horse training. I've noticed that they don't talk dominance/submission but they also don't let the horse back down from a problem either. They talk about gaining respect of the... show more So I'm stuck inside on a cold snowy day. As I'm flipping through the channels on the boob tube, I found a show on horse training. I've noticed that they don't talk dominance/submission but they also don't let the horse back down from a problem either. They talk about gaining respect of the horse. They also discuss harmony and partnership between the horse and rider. It seems like the dog training shows (there are not many) don't really discuss the actual partnership with the animal. Instead they speak dominance/submission.

The other thing that I have noticed is that the TV horse trainers appear to use all four squares in the operant conditioning quadrant. The TV dog trainers seem to use just positive reinforcement or positive punishment. Negative reinforcement or negative punishment don't seem to be a part of their methodology.

http://voices.yahoo.com/operant-conditio...
http://en.wikipedia.org/wiki/Operant_Con...

So my question: Do you feel that horse trainers are ahead of dog trainers in the way that they understand the animal and training in general? Why or why not?

Again no TDs from me.
Update: Cookie I have worked with horses, cattle and sheep. I've even trained a chicken or two and a goat. My question was based on the TV trainers. I know of quite a few horse trainers that use the "old" style of training which can be pretty brutal. I also did not TD you.
Update 2: Everyone answered the question beautifully. I'm going to put this up for the vote.
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