While Barton lessons utilize the tried and true Orton Gillingham techniques, there is actually quite a difference in the way the lessons are delivered. Barton lessons are prefabricated lessons that are used for all students. While I'm sure there are some tutors out there who tweak the lessons based off of their students needs, most of the time the lessons are delivered as-is with no consideration into what your child might specifically need. These tutors have typically gone through a training on how to deliver Barton lessons but no targeted training for OG.
An Orton Gillingham tutor on the other hand should have extensive training on the techniques of OG and an understanding of the why and when they should be used. An OG tutor creates individualized lessons for your child specifically. This will not only save you time and money, but it will get your child reading and writing up to speed a lot faster which will ultimately give them their confidence and time back to pursue the things they love.