To answer the OP, it really depends on what you’re looking for. You sound like a dressage rider who wants to use western tack, so my suspicion is that you’d better suit the WD side of things. Even then, be very careful given there are lots of dressage instructors playing cowboy dress up, so keep in mind you’ll be learning with that slant. There are some people who’ve managed to seem far more qualified than they are by teaching to a crowd with little dressage education – (ie) they wouldn’t get away with that in the normal dressage world.
If you actually want to learn to properly use western specific tack (western curbs/spades/hackamores), you’re slightly more likely to find good help in the CD camp. Eitan and instructors with his mindset are really only teaching “western” habits in as much as the old cowboy westerns ala Will Rogers are western – far more showy and “singing cowboy” oriented. If you really want good, educated, working cowboy education, look up the Sanders family (Katrina and Jeff). They’re teaching things that aren’t strictly limited to being useful in the show pen, rather than most whose teaching would break down if you tried to use it working cattle outside for 10 hours.
In both groups, avoid the people who are slanted to the western pleasure side of the gait spectrum, or who are convinced they’re bringing the light of dressage to the unwashed western masses. I’d also look for folks who can play nice with others.
WD and CD are doing great things to boost attendance at dressage shows, but as to whether they’re making better western horses, I’m not really very convinced. Little would hold up doing things that working cowboys would do in the fields. There are better places to find that (the California Bridlehorse Association for ex), but not everybody’s looking for that.