How do I run the numbers to figure out buying vs renting?

How do I figure out how many years do I have to own a home so that it becomes cheaper than renting?

I am PCSing in a few months to a HCOL area. Been looking online, someone gave the 5% rule, another gave the 8.71% rule. These rules say you multiply the cost of the house by these numbers and divide by 12, but it doesn’t seem accurate in terms of how much principal you start paying over time.

My BAH will be 3120, but if I subtract let’s say 300 for utilities, then it’s 2820 for comparable rent in public housing.

Houses are around 550k

Yearly fees that don’t go to principal

-1.25% for state tax
-1% maintenance cost
-1400 or .25% for insurance
-6.6% interest on va home loan

So is this 9.1% losses of the home purchase?

Thank you for your time.