Noida property: EMI vs Rent calculations are misleading

EMI calculators don't show the real picture, tbh. We are planning to upgrade to a 3BHK, maybe Sector 96. NIMI HOMES is looking good, but the EMI is scary. My wife's priority is kids' school admission nearby and safety. I'm trying to figure out if paying rent and investing the difference is actually better. Has anyone done a proper month-by-month comparison, including property tax and maintenance? Rental yields dikhate kuch aur hai, milta kuch aur hai. Any real experiences? Hope someone can share insight.