Shelby, I'm not an experienced rider by *any* means (new adult rider, maybe 6 months in!) but I can say this with confidence -- because I went through the wringer and back finding good instruction:
The foundations are the same, regardless of discipline. At a beginner level, the goal is simply a good seat, basic horse knowledge, healthy experience, and the resulting educated confidence that comes from it, so that you CAN begin to learn more advanced methods.
If after lessons you feel more afraid than confident, more angry/depressed/frustrated than "I'm having fun!", or if you're getting hurt in ways that really shouldn't be happening at lower levels (repeatedly falling off as a rank beginner, outside of freak accidents beyond human control, really should NOT happen) -- then the lessons aren't working. It doesn't matter why, or whose "fault" it is -- horse, rider, instructor -- the point is that instructor/horse/rider combo doesn't work, and you need to change up at least one of the components.
By the same token, if you feel happy about your lessons, if they feel like progress, if you find yourself daydreaming at work about your next one, and you feel SAFE and FUN and that awesome sense of accomplishment that comes from learning -- then they're right for you, regardless of the style!
It sounds like you might have found that with this latest place so follow your instincts -- don't fret over the method and just listen to your feelings. Safe, happy, fun + learning + horses/stable all look healthy, happy, and clean == New Lesson Barn. :)