Well they are different companies, so they're not required to charge similar prices. The shop that charges more may feel that they provide a better quality product (in this case a better learning experience). If you feel they are offering the same quality of service and product, then go with the cheaper shop…but don’t sacrifice quality for price!
Is the shop that charges less new? Sometimes new shops massively undercut their competitors to get a customer base....kinda a d**k move though...
Most shops determine price by adding instructor cost, materials cost, travel cost and some desired amount of profit (essentially what all business do). The shop that charges more may pay higher rent or pay their instructors better (though I doubt it), or may have some other expense. They may also just be greedy.
The shop that charges less may also be a 'gear' shop, that is once you're in the class they may have a constant, heavy sales pitch to get you to buy gear. I realize you said you own gear but that may just be how they come to the price for their course.