Yes, this is very true for all 1500s vs 2500s from 2015 and prior. But from my perspective the situation has changed a bit now, especially with $5.50 diesel while gas is $4 or less (here in Michigan anyway).
A new F250 7.3L gas will generally be within a couple mpg of the much more complicated, expensive to buy, fuel and maintain 6.7L scorpion for cruising and towing loads under ~12,000 lbs now.
A new GMC 6.6L gas has a similar comparison to the L5P duramax. They are really close.
It sucks that EPA regulations for diesel emissions have choked them so far from maximum efficiency, but it is what it is. 8 and 10 speed transmissions and better tuned manifolds, cyl heads and fuel injection have brought the gas motors really close to diesel in efficiency under load. Without the complications of a huge heavy motor with turbos, all the extra plumbing, emissions aftertreatment, etc.
By the way is anything wrong with your 6.2L? lol. My '03 6.0L LQ4 with 4L80 trans can still get 8-9 mpg with a 10k trailer load. But also still gets 9 mpg with my 5000 lb camper (aerodynamics mean a lot more than weight at highway speed).