The fuck? No they arent. The differences are the greatest between rank divisions. Non Com, NCO, SNCO, SSNCO. Co, Field, Generals. Pvt's and Generals dont live next door to each other because Generals get more money for BAH than Pvt's do.
No, that is because they make more money and decided where and how they want to live on their own.
Oh, and by far most Generals live on base housing. As most bases have specific housing set aside for flag officers.
If the Privates are not living next to Generals, that is mostly because the Private makes a whopping $2,100 a month while the General is making over $14,000 a month. And the General simply decided for one reason or another to live where a Private could afford.
Back in 1987 I bought a decent house in North Carolina. I was a Corporal, my next door neighbor was a Chief Petty Officer (E-7), the guy across the street was a Captain. Next to him lived a Staff Sergeant. Not to far away was indeed a Lieutenant Colonel. All of our houses were roughly the same price (around $55k), but the biggest difference was largely in our cars. My wife and I had older cars, they all had newer cars.
But the difference in pay by far outweighs the BAH. In my entire career I never once purchased or rented a home based upon my BAH. It was simply what I could afford based upon my
total pay.
And it is largely the same way on base housing. Yes, in the past it was much more separated by rank, but not as much today. Today the biggest difference is family size. So you may find a Captain with 3 kids living right next to a Sergeant with 3 kids, as that would require normally at least a 3 or 4 bedroom unit. And you might find a married Private with no kids living next to a married Captain with no kids. As both only merit a one bedroom unit.
Only in the older bases will you still find the housing separated by rank. Fort Bliss still has a "high ranking officers" area, but all the rest is more for the size of family than anything else. And all of the newest housing they have been building there since 2001 is "all ranks". Only Battalion Commanders and higher actually have a house assigned to them regardless of their family size. I know my old Battalion CO did not live in the house she rated, because she was single (divorced with a grown daughter) and did not see the need for a small 5 bedroom mansion just for herself. She just rented a nice apartment out in town.
And the Battalion CO that replaced her actually lived in a house he had bought over a decade before, so also did not use the mansion. I want to say there are around 30 mansions on Fort Bliss, and at any time 4 or 5 were always vacant because for one reason or another the person that rated it simply decided to live elsewhere.