This is and isn't true. They absolutely, positively do not get paid extra to live in a poor barracks as an allowance. An E-5 for one branch is going to be given the same allowance as another E-5. What CAN happen, however, is that the Defense Department can say that the living arrangements are shit and cap the amount of their allowance they have to pay at 75% of their allowance, effectively giving them extra pay for living in a bad situation.
That said, the Air Force has way nicer accommodations for one simple reason: it's an all volunteer force, even under the draft, and it's members tend to have skills that would allow them to live very well in the private sector if they decided to leave. So the Chair Force gets nicer perks because the alternative is spending millions to teach guys to fly and maintain aircraft... guys who have every incentive to leave once their 4 years are up to pull in serious money with the airlines. About the only other MoS that compares are other pilots, other mechanics, and medics who get free medical training that schools will honor to get a degree.